Dec 112017

Amortization Calculator and Table. | |||
---|---|---|---|

File Name | File Size | Zip Size | Zip Type |

AMORTIZE.EXE | 197588 | 121260 | deflated |

README.TXT | 20811 | 5978 | deflated |

# Download File VBAMORT.ZIP Here

## Contents of the README.TXT file

Amortization Calculator and Table.

Created by MJW Services.

(c) MJW Services 1993

This text file will provide useful examples on how to use the

software to solve complex financial problems. The software is not

the only item which is needed to complete these types of problems.

A pencil and paper for note taking will help create a powerful

financial tool useful for many different situations.

The text file is broken down into (6) catagories as follows

1. Special Notes

2. Amortization of a debt.

3. Mortgages.

4. Calculating the Outstanding Principal and Total Interest on debt.

5. Refinancing a loan.

6. Credit cards.

1. Special Notes

Disclaimer, Warranty and Copyright

----------------------------------

While this software is easy to use, financial planning requires

careful examination. MJW Services specifically disclaims all expressed

or implied warranties, including but not limited to, implied warranties

of merchantability and fitness for a particular use. In no event

shall MJW Services be liable for any loss of profit or any other

commercial damage. You should obtain professional guideance when making

any major financial decisions. MJW Services will not be responsible

for your interpretations of the results obtained with these routines,

even, in the unlikely event, it is shown that there is an error in the

programming of a particular routine. If you are about to make what

could be for you an important financial decision, always carefully

recheck the results obtained with this or any calculator.

For Non-Demo version only

-------------------------

This software is protected by Canadian copyright law. You must

treat this software like a "book", except you can make backup copies

for the purpose of protecting it from loss. Treating the software

like a "book" means that it can be used by anybody, and can be moved

from one computer to another, but just as a book cannot be used by

two people, at two different places, at the same time, neither can

this software (unless the copyright has been violated).

Calculation Notes

-----------------

Please keep in mind that the calculations happening inside

your machine are not rounded. All of the internal variables can

hold 15 or 16 digit numbers when the calculations are being performed

(only the digits being displayed on the screen are rounded, decimals

0 to 4 are rounded down and 5 to 9 are rounded up). When the table

is displayed, the numbers in each coloumn are rounded but that number

(which is used for the next calculation internally within the "loop"

is not rounded). When you calculate the Payment amount, the Number

of Payments final amount or the FVPrincipal ,the dollar figures are

displayed showing 4 digit decimals. This is necessary so that you are

able to perform the common financial practice of rounding up to the

nearest cent, regardless of the decimal (unless the 10th and 100th of

a cent decimals are 00 of course). You can still round down for

0 to 4 and up for 5 to 9 if you wish.

The results are very accurate.

Remember, an Amortization is a series of periodic payments,

usually equal, being made to reduce an outstanding debt. It is assumed

in this program, that the first payment being made on the loan

amount will be made exactly 1 payment period after the loan is issued.

The payment period is determined by the 'Payment Made' option.

If this procedure is not followed, the Dates on the Amortization Table

and the Amounts in the table will not be correct.

For the calculator, turning the Num Lock on and using the number

keypad is the easiest way to use it. The 'Backspace' key works as the

clear/clear error key and 'Enter' can be used for Equal.

You can use the Scrolling help box as an area where you can

take little notes, record numbers, etc. Don't worry about erasing

any words inside the box; they will be restored whenever you

run the program. Keep in mind that any notes you put inside of

the box WILL NOT be saved when you exit the program.

The examples contained within this text file will provide you

with some insight on how to reach an accurate solution using this

program. Only certain portions of the following can be calculated

with the demo version.

2. Amortization of a debt

The Amortization method is used to eliminate an interest bearing

debt by making a series of periodic payments (usually equal payments).

When a debt is amortized by equal payments at equal payment intervals,

the debt is actually the discounted value of an annuity. The size of

the payment is determined by annuity methods.

eg.1. A loan of $10000 is to be amortized with equal monthly

payments over a period of 10 years. The interest rate

is 10% compounded monthly. Find the value of the

concluding payment.

solution: Enter information into appropriate fields.

Principal = 10000

Interest rate = .10

Number of payments = 12 payments x 10 years = 120

Select Rate Compounded Monthly option and

Payment Made monthly option.

Tab to Payment Amount command ( or Alt-a to immediately

execute the command) and press Enter.

The result is $132.1507. Rounding up to the nearest cent

we get $132.16. Tab to the Payment input field( or Alt-y to

immediately jump to it) and enter the number 132.16. Tab to

the Number of Payments command (or Alt-u to immediately

execute the command) and press enter. The result is 119

equal payments of $132.16 and 1 final payment of $130.2625.

Rounding the final payment up to the nearest cent, the final

payment is $130.27. Verify this result with what the

Amortization Table displays and you can see that the 120th

final payment is $130.27 (129.19 + 1.08).

eg.2. A loan of $5000 will be repaid over 3 years by making quarterly

payments. The interest rate is 12% compounded monthly. Find

the quarterly payment and show the interest and principal

portion of each payment.

solution: Enter information into appropriate fields.

Principal = 5000

Interest rate = .12

Number of payments = 4 payments x 3 years = 12

Select Rate Compounded Monthly option and

Payment Made quarterly option.

Tab to Payment Amount command ( or Alt-a to immediately

execute the command) and press Enter.

The result is $503.2134 (rounding up to the nearest cent

we get $503.22).Tab to the Table command and press Enter.

The program will ask you to enter the date when

the payments begin. By default, the program will display

your system date, so just Tab to the OK button and press

enter if the date is not important. We can see the

interest portion and the principal repayment for each payment.

eg.3. A $3000 loan will be repaid by monthly payments of $600 for as

long as necessary with the first payment being made at the end

of 6 months. The interest rate is 13% compounded monthly. Find

the size of the debt at the end of 5 months and produce an

Amortization Table.

solution: Enter information into appropriate fields.

Principal = 3000

Interest rate = .13

Number of payments = 5

Select Rate Compounded Monthly option and

Payment Made monthly option.

Tab to the FVPrincipal command (Future Value of a Principal,

or Alt-f to immediately execute) and press Enter.

The result is $3166.0592 (rounding up to the nearest cent

we get $3166.06). This amount is the value of $3000 at 13%

interest compounded monthly for 5 months. The payments have

been deferred for 6 months but the interest will still

accumulate for the 5 months prior to the start of the

amortization. $3166.06 is the amount of the loan which will

be amortized by making monthly payments of $600 for as

long as necessary. Enter 3166.06 as the Principal amount

of the loan. Enter 600 as the amount of the Payment on

the loan each period (the other information will remain the

same since the rate, compounding period, or payment made time

period are not changing). Tab to the Number of Payments

button and press Enter. The result is 5 equal payments of

$600 and 1 payment of $278.5888(rounding up to the nearest

cent we get $278.59). Tab to the Table button that has

appeared and press Enter to view the Amortization Table.

3. Mortgages

This section will give insight into using the software to calculate

Mortgages in Canada.

eg.1. In mid 1979, mortgage rates in Canada averaged around 11%

compounded semi-annually. Two years later, interest rates

rose to 22% compounded semi-annually. On a mortgage of

$40000, determine the monthly payment over a 20 year

mortgage for both rates of interest.

solution: Enter the information for the first mortgage.

Principal = 40000

Interest Rate = .11

Number or Payments = 12 payments x 20 years = 240

Select Rate Compounded Semi-Annually and Payments Made

monthly options.

Tab to Payment Amount and press Enter (or Alt-a to

immediately execute). The result is $406.2559 or rounded

$406.26 per month.

Enter the information for the second mortgage.

All information remains the same except for:

Interest Rate = .22

Enter this amount then tab to Payment Amount.

The result is $712.7850 or rounded up $712.79 per month.

eg.2. A couple buys a house worth $102000 by paying $52000 down and

taking a mortgage for $50000. The interest rate is 9%

compounded semi-annually, and they will make monthly payments

over a 25 year period. Determine the amount of the debt paid

off in the first year.

solution: Enter the information for the problem

Principal = 50000

Interest Rate = .09

Number of Payments = 12 payments x 25 years = 300

Selct Interest Compounded Semi-Annually and Payments

Made Monthly.

Tab over to (or press Alt-a to immediately execute) the

Payment Amount button and press Enter. The monthly

payment is $413.9887 (or $413.99 rounded up). Tab to the

Table button that has appeared on the screen and press

Enter to display the Amortization Table. We can see

the Ending Principal amount for the 12th payment is

$49427.18. Subtracting this number from the original

Principal amount we get $50000 - $49427.18 = $572.82

which is the amount of Principal paid off after the

first year.

4. Calculating the Outstanding Principal and Total Interest at a point

in time.

The Amortization Table is very useful for calculating Outstanding

Principal amounts, Principal Repayment and Interest charged,

and Total Interest paid at a particular point in time. The

following example will show you how to use these calculations.

eg.1 A car is purchased for $15000 by paying $6000 down and then

equal monthly payments for 3 years at 15% interest compounded

monthly. Find the Outstanding Principal Amount and the

amount of interest paid after the first year.

solution: Enter the information:

Principal Amount = 15000 - 6000 = 9000

Interest rate = .15

Number of Payments = 12 payments x 3 years = 36

Select Interest Compounded monthly and Payments made

monthly.

Tab over to the Payment Amount button and press

Enter. The monthly payment will be $311.9880(rounded up

$311.99. Tab over to the Table button that has appeared

and press Enter to display the Amortization Table.

The Ending Principal at the 12th payment is $6434.51 and

the Total Interest paid on the loan at the 12th payment

is $1178.37.

5. Refinancing a loan

The power of this software is greatly increased by the

user's ability to logically pick out all the information

to complete a complex financial problem. Once it is broken

down into smaller parts, knowing what to do with the parts

is the key to solving a difficult problem. Knowledge of financial

mathematics is not required to arrive at the correct solution

(the program takes care of that for you). The following

questions will demonstrate how to use the software to determine

whether refiancing a loan is the correct option to pick.

eg.1. Fred buys $6500 worth of furniture from Joe's Furniture Store.

He pays $500 down and agrees to pay off the balance with

monthly payments over 5 years. The interest rate Joe's

Furniture Store charges is 16% compounded monthly. The

payment agreement states that if Fred wishes to pay off the

remaining balance early, a penalty will be charged equal to

3 months' payments. After 2 years, Fred determines

that he can borrow the money from a bank at 10% compounded

monthly, but will also have to pay the 3 month penalty.

Should he refinance?

solution: The first thing which needs to be done to solve this

problem will be to enter the information required

to determine the size of the monthly payments Fred

will be required to pay over the 5 year period.

Principal = 6500 - 500 = 6000

Interest Rate = .16

Number of Payments = 12 payments x 5 years = 60

Select Interest compounded monthly and Payment

made monthly.

Tab over to the Payment Amount and press Enter (

or Alt-a to immediately execute). The monthly

payment amount is $145.9083 (rounded up $145.91).

We can now determine the penalty that Fred will have

to pay if he pays off the balance owing to the

furniture company early.

$145.91 x 3 = $437.73 is 3 months worth of payments

and is the amount of the penalty.

After paying $145.91 per month for 2 years, Fred realizes

that he can borrow money from the bank at a lower rate.

Here, we Tab to the Table button that has appeared and

press enter to display the Amortization Table. At the

24th monthly payment, the ending balance of the loan is

$4150.19. Since paying off this amount will result in

the penalty being assessed, we will add the penalty amount

to the ending balance of the loan after 2 years to

determine the amount of money to be borrowed from the bank.

$4150.19 + 437.73 = $4587.92

The $4587.92 is the amount that now will be amortized over

the remaining 3 years (since 2 years have already been

paid off of the 5 year monthly payment schedule).

Scroll the Amortization Table to the end and re-enter the

new information into the program.

Principal = 4587.92

Interest Rate = .10

Number of Payments = 12 payments x 3 years = 36

The compound period remains the same as does the

monthly payment.

Tab to the Payment Amount and press Enter.

We can see that the new Payment amount is

$148.0393 (rounded up $148.04).

It would not be a wise financial move for Fred

to refinance the loan since his monthly payment

will go up by $2.13. ($148.04 - $145.91)

eg.2. A five year bank loan for $8500 is being amortized with monthly

payments at 15% compounded monthly. Just after making the 30th

payment, the borrower has the remaining principal refinanced

at 11% compounded monthly with the term of the loan remaining

unchanged. Find the monthly savings in interest.

solution: Enter the information:

Principal = 8500

Interest Rate = .15

Number of Payments = 12 payments x 5 years = 60

Select Interest compounded monthly and Payments Made

monthly options.

Tab to Payment Amount and press Enter.

The monthly payment is $202.2144(rounded up 202.22).

Tab to the Table button that has appeared and press

Enter to display the Amortization Table.

After the 30th payment, the Ending Principal is

$5032.90. This is the amount to be refinanced at

11%

Enter the new information:

Principal = 5032.90

Interest Rate = .11

Number of payments = 30

Compound period and Payment period do not change.

Tab to the Payment Amount and press Enter to see

the new monthly payment. It is $192.6497 (rounded

up $192.65)

Now we can find the monthly savings in interest

$202.22 - $192.65 = $9.57

6. Credit Cards

Interest rates on Credit Card balances outstanding are

compounded daily. The higher the frequency of the compounding,

given a fixed Principal amount and Interest rate, the faster

the interest accumulates.

eg.1. John has a credit card that charges interest at 16.75% compounded

daily. On March 17th, he uses the card at a bank machine

for a cash advance of $400. If the statement date is April 15th,

what will be the balance outstanding on the credit card as of

that date (assuming no other charges have been incurred and

no fee has been assessed by the bank for a cash advance)?

If he pays $40 per month on the credit card, how long will

it take for him to pay off the balance and what is the

amount of the final payment?

Solution: Enter the information

Principal = 400

Interest Rate = .1675

Number of Periods = 30

Day 1 is the day the cash was advanced (Mar 17) and day 30

is the statement date ( April 15)

Select the Rate Compounded daily option.

Remember, we are calculating the Future value of an amount

so we will be using the FVPrincipal button for the

calculation. When this button is used, the Number of

Payments input area is actually the number of

interest compound periods.

Tab to the FVPrincipal button and press Enter.

The result is $405.5436 rounded up is $405.55 which is

the balance on the card.

Remember that the digits used internally for this program

(and the daily interest rate) are 15 or 16 digits long

so the result is very accurate. Companies that issue

credit cards sometimes round off the daily interest

compounding rate to 5, 6, or 7 digits. When this is

the case, what you see on your statement as interest

charges may vary slightly from the results produced

by this software.

Input the information back into the program

Principal = 405.55

Interest rate = .1675

Payment amount = 40

Make sure the interest compounded period is set to daily

and the payments made option button is set to monthly.

Tab to the Number of Payments button and press Enter.

The result is 11 equal payments of $40 and 1 payment of

59 cents.

Created by MJW Services.

(c) MJW Services 1993

This text file will provide useful examples on how to use the

software to solve complex financial problems. The software is not

the only item which is needed to complete these types of problems.

A pencil and paper for note taking will help create a powerful

financial tool useful for many different situations.

The text file is broken down into (6) catagories as follows

1. Special Notes

2. Amortization of a debt.

3. Mortgages.

4. Calculating the Outstanding Principal and Total Interest on debt.

5. Refinancing a loan.

6. Credit cards.

1. Special Notes

Disclaimer, Warranty and Copyright

----------------------------------

While this software is easy to use, financial planning requires

careful examination. MJW Services specifically disclaims all expressed

or implied warranties, including but not limited to, implied warranties

of merchantability and fitness for a particular use. In no event

shall MJW Services be liable for any loss of profit or any other

commercial damage. You should obtain professional guideance when making

any major financial decisions. MJW Services will not be responsible

for your interpretations of the results obtained with these routines,

even, in the unlikely event, it is shown that there is an error in the

programming of a particular routine. If you are about to make what

could be for you an important financial decision, always carefully

recheck the results obtained with this or any calculator.

For Non-Demo version only

-------------------------

This software is protected by Canadian copyright law. You must

treat this software like a "book", except you can make backup copies

for the purpose of protecting it from loss. Treating the software

like a "book" means that it can be used by anybody, and can be moved

from one computer to another, but just as a book cannot be used by

two people, at two different places, at the same time, neither can

this software (unless the copyright has been violated).

Calculation Notes

-----------------

Please keep in mind that the calculations happening inside

your machine are not rounded. All of the internal variables can

hold 15 or 16 digit numbers when the calculations are being performed

(only the digits being displayed on the screen are rounded, decimals

0 to 4 are rounded down and 5 to 9 are rounded up). When the table

is displayed, the numbers in each coloumn are rounded but that number

(which is used for the next calculation internally within the "loop"

is not rounded). When you calculate the Payment amount, the Number

of Payments final amount or the FVPrincipal ,the dollar figures are

displayed showing 4 digit decimals. This is necessary so that you are

able to perform the common financial practice of rounding up to the

nearest cent, regardless of the decimal (unless the 10th and 100th of

a cent decimals are 00 of course). You can still round down for

0 to 4 and up for 5 to 9 if you wish.

The results are very accurate.

Remember, an Amortization is a series of periodic payments,

usually equal, being made to reduce an outstanding debt. It is assumed

in this program, that the first payment being made on the loan

amount will be made exactly 1 payment period after the loan is issued.

The payment period is determined by the 'Payment Made' option.

If this procedure is not followed, the Dates on the Amortization Table

and the Amounts in the table will not be correct.

For the calculator, turning the Num Lock on and using the number

keypad is the easiest way to use it. The 'Backspace' key works as the

clear/clear error key and 'Enter' can be used for Equal.

You can use the Scrolling help box as an area where you can

take little notes, record numbers, etc. Don't worry about erasing

any words inside the box; they will be restored whenever you

run the program. Keep in mind that any notes you put inside of

the box WILL NOT be saved when you exit the program.

The examples contained within this text file will provide you

with some insight on how to reach an accurate solution using this

program. Only certain portions of the following can be calculated

with the demo version.

2. Amortization of a debt

The Amortization method is used to eliminate an interest bearing

debt by making a series of periodic payments (usually equal payments).

When a debt is amortized by equal payments at equal payment intervals,

the debt is actually the discounted value of an annuity. The size of

the payment is determined by annuity methods.

eg.1. A loan of $10000 is to be amortized with equal monthly

payments over a period of 10 years. The interest rate

is 10% compounded monthly. Find the value of the

concluding payment.

solution: Enter information into appropriate fields.

Principal = 10000

Interest rate = .10

Number of payments = 12 payments x 10 years = 120

Select Rate Compounded Monthly option and

Payment Made monthly option.

Tab to Payment Amount command ( or Alt-a to immediately

execute the command) and press Enter.

The result is $132.1507. Rounding up to the nearest cent

we get $132.16. Tab to the Payment input field( or Alt-y to

immediately jump to it) and enter the number 132.16. Tab to

the Number of Payments command (or Alt-u to immediately

execute the command) and press enter. The result is 119

equal payments of $132.16 and 1 final payment of $130.2625.

Rounding the final payment up to the nearest cent, the final

payment is $130.27. Verify this result with what the

Amortization Table displays and you can see that the 120th

final payment is $130.27 (129.19 + 1.08).

eg.2. A loan of $5000 will be repaid over 3 years by making quarterly

payments. The interest rate is 12% compounded monthly. Find

the quarterly payment and show the interest and principal

portion of each payment.

solution: Enter information into appropriate fields.

Principal = 5000

Interest rate = .12

Number of payments = 4 payments x 3 years = 12

Select Rate Compounded Monthly option and

Payment Made quarterly option.

Tab to Payment Amount command ( or Alt-a to immediately

execute the command) and press Enter.

The result is $503.2134 (rounding up to the nearest cent

we get $503.22).Tab to the Table command and press Enter.

The program will ask you to enter the date when

the payments begin. By default, the program will display

your system date, so just Tab to the OK button and press

enter if the date is not important. We can see the

interest portion and the principal repayment for each payment.

eg.3. A $3000 loan will be repaid by monthly payments of $600 for as

long as necessary with the first payment being made at the end

of 6 months. The interest rate is 13% compounded monthly. Find

the size of the debt at the end of 5 months and produce an

Amortization Table.

solution: Enter information into appropriate fields.

Principal = 3000

Interest rate = .13

Number of payments = 5

Select Rate Compounded Monthly option and

Payment Made monthly option.

Tab to the FVPrincipal command (Future Value of a Principal,

or Alt-f to immediately execute) and press Enter.

The result is $3166.0592 (rounding up to the nearest cent

we get $3166.06). This amount is the value of $3000 at 13%

interest compounded monthly for 5 months. The payments have

been deferred for 6 months but the interest will still

accumulate for the 5 months prior to the start of the

amortization. $3166.06 is the amount of the loan which will

be amortized by making monthly payments of $600 for as

long as necessary. Enter 3166.06 as the Principal amount

of the loan. Enter 600 as the amount of the Payment on

the loan each period (the other information will remain the

same since the rate, compounding period, or payment made time

period are not changing). Tab to the Number of Payments

button and press Enter. The result is 5 equal payments of

$600 and 1 payment of $278.5888(rounding up to the nearest

cent we get $278.59). Tab to the Table button that has

appeared and press Enter to view the Amortization Table.

3. Mortgages

This section will give insight into using the software to calculate

Mortgages in Canada.

eg.1. In mid 1979, mortgage rates in Canada averaged around 11%

compounded semi-annually. Two years later, interest rates

rose to 22% compounded semi-annually. On a mortgage of

$40000, determine the monthly payment over a 20 year

mortgage for both rates of interest.

solution: Enter the information for the first mortgage.

Principal = 40000

Interest Rate = .11

Number or Payments = 12 payments x 20 years = 240

Select Rate Compounded Semi-Annually and Payments Made

monthly options.

Tab to Payment Amount and press Enter (or Alt-a to

immediately execute). The result is $406.2559 or rounded

$406.26 per month.

Enter the information for the second mortgage.

All information remains the same except for:

Interest Rate = .22

Enter this amount then tab to Payment Amount.

The result is $712.7850 or rounded up $712.79 per month.

eg.2. A couple buys a house worth $102000 by paying $52000 down and

taking a mortgage for $50000. The interest rate is 9%

compounded semi-annually, and they will make monthly payments

over a 25 year period. Determine the amount of the debt paid

off in the first year.

solution: Enter the information for the problem

Principal = 50000

Interest Rate = .09

Number of Payments = 12 payments x 25 years = 300

Selct Interest Compounded Semi-Annually and Payments

Made Monthly.

Tab over to (or press Alt-a to immediately execute) the

Payment Amount button and press Enter. The monthly

payment is $413.9887 (or $413.99 rounded up). Tab to the

Table button that has appeared on the screen and press

Enter to display the Amortization Table. We can see

the Ending Principal amount for the 12th payment is

$49427.18. Subtracting this number from the original

Principal amount we get $50000 - $49427.18 = $572.82

which is the amount of Principal paid off after the

first year.

4. Calculating the Outstanding Principal and Total Interest at a point

in time.

The Amortization Table is very useful for calculating Outstanding

Principal amounts, Principal Repayment and Interest charged,

and Total Interest paid at a particular point in time. The

following example will show you how to use these calculations.

eg.1 A car is purchased for $15000 by paying $6000 down and then

equal monthly payments for 3 years at 15% interest compounded

monthly. Find the Outstanding Principal Amount and the

amount of interest paid after the first year.

solution: Enter the information:

Principal Amount = 15000 - 6000 = 9000

Interest rate = .15

Number of Payments = 12 payments x 3 years = 36

Select Interest Compounded monthly and Payments made

monthly.

Tab over to the Payment Amount button and press

Enter. The monthly payment will be $311.9880(rounded up

$311.99. Tab over to the Table button that has appeared

and press Enter to display the Amortization Table.

The Ending Principal at the 12th payment is $6434.51 and

the Total Interest paid on the loan at the 12th payment

is $1178.37.

5. Refinancing a loan

The power of this software is greatly increased by the

user's ability to logically pick out all the information

to complete a complex financial problem. Once it is broken

down into smaller parts, knowing what to do with the parts

is the key to solving a difficult problem. Knowledge of financial

mathematics is not required to arrive at the correct solution

(the program takes care of that for you). The following

questions will demonstrate how to use the software to determine

whether refiancing a loan is the correct option to pick.

eg.1. Fred buys $6500 worth of furniture from Joe's Furniture Store.

He pays $500 down and agrees to pay off the balance with

monthly payments over 5 years. The interest rate Joe's

Furniture Store charges is 16% compounded monthly. The

payment agreement states that if Fred wishes to pay off the

remaining balance early, a penalty will be charged equal to

3 months' payments. After 2 years, Fred determines

that he can borrow the money from a bank at 10% compounded

monthly, but will also have to pay the 3 month penalty.

Should he refinance?

solution: The first thing which needs to be done to solve this

problem will be to enter the information required

to determine the size of the monthly payments Fred

will be required to pay over the 5 year period.

Principal = 6500 - 500 = 6000

Interest Rate = .16

Number of Payments = 12 payments x 5 years = 60

Select Interest compounded monthly and Payment

made monthly.

Tab over to the Payment Amount and press Enter (

or Alt-a to immediately execute). The monthly

payment amount is $145.9083 (rounded up $145.91).

We can now determine the penalty that Fred will have

to pay if he pays off the balance owing to the

furniture company early.

$145.91 x 3 = $437.73 is 3 months worth of payments

and is the amount of the penalty.

After paying $145.91 per month for 2 years, Fred realizes

that he can borrow money from the bank at a lower rate.

Here, we Tab to the Table button that has appeared and

press enter to display the Amortization Table. At the

24th monthly payment, the ending balance of the loan is

$4150.19. Since paying off this amount will result in

the penalty being assessed, we will add the penalty amount

to the ending balance of the loan after 2 years to

determine the amount of money to be borrowed from the bank.

$4150.19 + 437.73 = $4587.92

The $4587.92 is the amount that now will be amortized over

the remaining 3 years (since 2 years have already been

paid off of the 5 year monthly payment schedule).

Scroll the Amortization Table to the end and re-enter the

new information into the program.

Principal = 4587.92

Interest Rate = .10

Number of Payments = 12 payments x 3 years = 36

The compound period remains the same as does the

monthly payment.

Tab to the Payment Amount and press Enter.

We can see that the new Payment amount is

$148.0393 (rounded up $148.04).

It would not be a wise financial move for Fred

to refinance the loan since his monthly payment

will go up by $2.13. ($148.04 - $145.91)

eg.2. A five year bank loan for $8500 is being amortized with monthly

payments at 15% compounded monthly. Just after making the 30th

payment, the borrower has the remaining principal refinanced

at 11% compounded monthly with the term of the loan remaining

unchanged. Find the monthly savings in interest.

solution: Enter the information:

Principal = 8500

Interest Rate = .15

Number of Payments = 12 payments x 5 years = 60

Select Interest compounded monthly and Payments Made

monthly options.

Tab to Payment Amount and press Enter.

The monthly payment is $202.2144(rounded up 202.22).

Tab to the Table button that has appeared and press

Enter to display the Amortization Table.

After the 30th payment, the Ending Principal is

$5032.90. This is the amount to be refinanced at

11%

Enter the new information:

Principal = 5032.90

Interest Rate = .11

Number of payments = 30

Compound period and Payment period do not change.

Tab to the Payment Amount and press Enter to see

the new monthly payment. It is $192.6497 (rounded

up $192.65)

Now we can find the monthly savings in interest

$202.22 - $192.65 = $9.57

6. Credit Cards

Interest rates on Credit Card balances outstanding are

compounded daily. The higher the frequency of the compounding,

given a fixed Principal amount and Interest rate, the faster

the interest accumulates.

eg.1. John has a credit card that charges interest at 16.75% compounded

daily. On March 17th, he uses the card at a bank machine

for a cash advance of $400. If the statement date is April 15th,

what will be the balance outstanding on the credit card as of

that date (assuming no other charges have been incurred and

no fee has been assessed by the bank for a cash advance)?

If he pays $40 per month on the credit card, how long will

it take for him to pay off the balance and what is the

amount of the final payment?

Solution: Enter the information

Principal = 400

Interest Rate = .1675

Number of Periods = 30

Day 1 is the day the cash was advanced (Mar 17) and day 30

is the statement date ( April 15)

Select the Rate Compounded daily option.

Remember, we are calculating the Future value of an amount

so we will be using the FVPrincipal button for the

calculation. When this button is used, the Number of

Payments input area is actually the number of

interest compound periods.

Tab to the FVPrincipal button and press Enter.

The result is $405.5436 rounded up is $405.55 which is

the balance on the card.

Remember that the digits used internally for this program

(and the daily interest rate) are 15 or 16 digits long

so the result is very accurate. Companies that issue

credit cards sometimes round off the daily interest

compounding rate to 5, 6, or 7 digits. When this is

the case, what you see on your statement as interest

charges may vary slightly from the results produced

by this software.

Input the information back into the program

Principal = 405.55

Interest rate = .1675

Payment amount = 40

Make sure the interest compounded period is set to daily

and the payments made option button is set to monthly.

Tab to the Number of Payments button and press Enter.

The result is 11 equal payments of $40 and 1 payment of

59 cents.

December 11, 2017
Add comments