Generating an Amortization Schedule Automatically

After entering the initial values for P1 and P2, you can compute an

amortization schedule automatically.

1. Press & \.

— or —

If INT is displayed, press # to display the current P1 value.

2. Press %. Both P1 and P2 update automatically to represent the

next range of payments.

The calculator computes the next range of payments using the same

number of periods used with the previous range of payments. For

example, if the previous range was 1 through 12 (12 payments),

pressing % updates the range to 13 through 24 (12 payments).

3. Press # to display P2.

• If you press % with P1 displayed, a new value for P2 will be

displayed automatically. (You can still enter a new value for P2.)

• If you did not press % with P1 displayed, you can press %

with P2 displayed to enter values for both P1 and P2 in the next

range of payments.

4. Press # to display each of the automatically computed values for

BAL, PRN, and INT in the next range of payments.

5. Repeat steps 1 through 4 until the schedule is complete.

Example: Computing Basic Loan Interest

If you make a monthly payment of $425.84 on a 30-year mortgage for

$75,000, what is the interest rate on your mortgage?

To Press Display

Set payments per year to 12. & [ 12 ! P/Y= 12.00

Return to standard-calculator

mode.

& U 0.00

Enter number of payments

using the payment multiplier.

30 & Z , N= 360.00

Answer: The interest rate is 5.5% per year.

Examples: Computing Basic Loan Payments

These examples show you how to compute basic loan payments on a

$75,000 mortgage at 5.5% for 30 years.

Note: After you complete the first example, you should not have to reenter

the values for loan amount and interest rate. The calculator saves

the values you enter for later use.

Computing Monthly Payments

Answer: The monthly payments are $425.84.

Computing Quarterly Payments

Note: The calculator automatically sets the number of compounding

periods (C/Y) to equal the number of payment periods (P/Y).

Enter loan amount. 75000 . PV= 75,000.00õ

Enter payment amount. 425.84 S / PMT= -425.84

Compute interest rate. % - I/Y= 5.50

To Press Display

Set payments per year to 12. & [ 12 ! P/Y= 12.00

Return to standard-calculator

mode.

& U 0.00

Enter number of payments

using payment multiplier.

30 & Z , N= 360.00

Enter interest rate. 5.5 - I/Y= 5.50

Enter loan amount. 75000 . PV= 75,000.00õ

Compute payment. % / PMT= -425.84

To Press Display

Set payments per year to 4. & [ 4 ! P/Y= 4.00

Return to standard-calculator

mode.

& U 0.00

Enter number of payments

using payment multiplier.

30 & Z , N= 120.00

To Press Display

Answer: The quarterly payments are $1,279.82.

Examples: Computing Value in Savings

These examples show you how to compute the future and present values

of a savings account paying 0.5% compounded at the end of each year

with a 20-year time frame.

Computing Future Value

Example: If you open the account with $5,000, how much will you have

after 20 years?

Answer: The account will be worth $5,524.48 after 20 years.

Computing Present Value

Example: How much money must you deposit to have $10,000 in 20

years?

Answer: You must deposit $9,050.63.

Compute payment. % / PMT= -1,279.82

To Press Display

Set all variables to defaults. & }

!

RST 0.00

Enter number of payments. 20 , N= 20.00

Enter interest rate. .5 - I/Y= 0.50

Enter beginning balance. 5000 S . PV= -5,000.00

Compute future value. % 0 FV= 5,524.48

To Press Display

Enter final balance. 10000 0 FV= 10,000.00

Compute present value. % . PV= -9,050.63

To Press Display

Time-Value-of-Money and Amortization Worksheets 29

Example: Computing Present Value in Annuities

The Furros Company purchased equipment providing an annual savings

of $20,000 over 10 years. Assuming an annual discount rate of 10%, what

is the present value of the savings using an ordinary annuity and an

annuity due?

Cost Savings for a Present-Value Ordinary Annuity

Cost Savings for a Present-Value Annuity Due in a Leasing

Agreement

To Press Display

Set all variables to defaults. & } ! RST 0.00

Enter number of payments. 10 , N= 10.00

Enter interest rate per

payment period.

10 - I/Y= 10.00

Enter payment. 20000 S / PMT= -20,000.00

Answer: The present value of the savings is $122,891.34 with an ordinary

annuity and $135,180.48 with an annuity due.

Example: Computing Perpetual Annuities

To replace bricks in their highway system, the Land of Oz has issued

perpetual bonds paying $110 per $1000 bond. What price should you pay

for the bonds to earn 15% annually?

Answer: You should pay $733.33 for a perpetual ordinary annuity and

$843.33 for a perpetual annuity due.

A perpetual annuity can be an ordinary annuity or an annuity due

consisting of equal payments continuing indefinitely (for example, a

preferred stock yielding a constant dollar dividend).

Perpetual ordinary annuity

Compute present value

(ordinary annuity).

% . PV= 122,891.34

Set beginning-of-period

payments.

& ] & V BGN

Return to calculator mode. & U 0.00

Compute present value

(annuity due).

% . PV= 135,180.48

To Press Display

Calculate the present value for a

perpetual ordinary annuity.

110 6 15 2 N 733.33

Calculate the present value for a

perpetual annuity due.

H 110 N 843.33

To Press Display

Perpetual annuity due

Because the term (1 + I/Y / 100)-N in the present value annuity equations

approaches zero as N increases, you can use these equations to solve for

the present value of a perpetual annuity:

• Perpetual ordinary annuity

• Perpetual annuity due

Example: Computing Present Value of Variable

Cash Flows

The ABC Company purchased a machine that will save these end-of-year

amounts:

Year 1 2 3 4

Amount $5000 $7000 $8000 $10000

PV PMT

I/Y100

= ---------------------------

PV PMT PMT

I/Y⁄100 

= + ----------------------------

Given a 10% discount rate, does the present value of the cash flows

exceed the original cost of $23,000?

To Press Display

Set all variables to defaults. & }

!

RST 0.00

Enter interest rate per cash flow

period.

10 - I/Y= 10.00

Enter 1st cash flow. 5000 S 0 FV= -5,000.00

Enter 1st cash flow period. 1 , N= 1.00

Compute present value of 1st cash

flow.

% . PV= 4,545.45

Store in M1. D 1 4,545.45

Enter 2nd cash flow. 7000 S 0 FV= -7,000.00

Enter 2nd cash flow period. 2 , N= 2.00

Compute present value of 2nd

cash flow.

% . PV= 5,785.12

Sum to memory. D H 1 5,785.12

Enter 3rd cash flow. 8000 S 0 FV= -8,000.00

Enter period number. 3 , N= 3.00

Compute present value of 3rd

cash flow.

% . PV= 6,010.52

Sum to memory. D H 1 6,010.52

Enter 4th cash flow. 10000 S 0 FV= -10,000.00

Enter period number. 4 , N= 4.00

Time-Value-of-Money and Amortization Worksheets 33

Answer: The present value of the cash flows is $23,171.23, which exceeds

the machine’s cost by $171.23. This is a profitable investment.

Note: Although variable cash flow payments are not equal (unlike

annuity payments), you can solve for the present value by treating the

cash flows as a series of compound interest payments.

The present value of variable cash flows is the value of cash flows

occurring at the end of each payment period discounted back to the

beginning of the first cash flow period (time zero).

Example: Computing Present Value of a Lease

After entering the initial values for P1 and P2, you can compute an

amortization schedule automatically.

1. Press & \.

— or —

If INT is displayed, press # to display the current P1 value.

2. Press %. Both P1 and P2 update automatically to represent the

next range of payments.

The calculator computes the next range of payments using the same

number of periods used with the previous range of payments. For

example, if the previous range was 1 through 12 (12 payments),

pressing % updates the range to 13 through 24 (12 payments).

3. Press # to display P2.

• If you press % with P1 displayed, a new value for P2 will be

displayed automatically. (You can still enter a new value for P2.)

• If you did not press % with P1 displayed, you can press %

with P2 displayed to enter values for both P1 and P2 in the next

range of payments.

4. Press # to display each of the automatically computed values for

BAL, PRN, and INT in the next range of payments.

5. Repeat steps 1 through 4 until the schedule is complete.

Example: Computing Basic Loan Interest

If you make a monthly payment of $425.84 on a 30-year mortgage for

$75,000, what is the interest rate on your mortgage?

To Press Display

Set payments per year to 12. & [ 12 ! P/Y= 12.00

Return to standard-calculator

mode.

& U 0.00

Enter number of payments

using the payment multiplier.

30 & Z , N= 360.00

Answer: The interest rate is 5.5% per year.

Examples: Computing Basic Loan Payments

These examples show you how to compute basic loan payments on a

$75,000 mortgage at 5.5% for 30 years.

Note: After you complete the first example, you should not have to reenter

the values for loan amount and interest rate. The calculator saves

the values you enter for later use.

Computing Monthly Payments

Answer: The monthly payments are $425.84.

Computing Quarterly Payments

Note: The calculator automatically sets the number of compounding

periods (C/Y) to equal the number of payment periods (P/Y).

Enter loan amount. 75000 . PV= 75,000.00õ

Enter payment amount. 425.84 S / PMT= -425.84

Compute interest rate. % - I/Y= 5.50

To Press Display

Set payments per year to 12. & [ 12 ! P/Y= 12.00

Return to standard-calculator

mode.

& U 0.00

Enter number of payments

using payment multiplier.

30 & Z , N= 360.00

Enter interest rate. 5.5 - I/Y= 5.50

Enter loan amount. 75000 . PV= 75,000.00õ

Compute payment. % / PMT= -425.84

To Press Display

Set payments per year to 4. & [ 4 ! P/Y= 4.00

Return to standard-calculator

mode.

& U 0.00

Enter number of payments

using payment multiplier.

30 & Z , N= 120.00

To Press Display

Answer: The quarterly payments are $1,279.82.

Examples: Computing Value in Savings

These examples show you how to compute the future and present values

of a savings account paying 0.5% compounded at the end of each year

with a 20-year time frame.

Computing Future Value

Example: If you open the account with $5,000, how much will you have

after 20 years?

Answer: The account will be worth $5,524.48 after 20 years.

Computing Present Value

Example: How much money must you deposit to have $10,000 in 20

years?

Answer: You must deposit $9,050.63.

Compute payment. % / PMT= -1,279.82

To Press Display

Set all variables to defaults. & }

!

RST 0.00

Enter number of payments. 20 , N= 20.00

Enter interest rate. .5 - I/Y= 0.50

Enter beginning balance. 5000 S . PV= -5,000.00

Compute future value. % 0 FV= 5,524.48

To Press Display

Enter final balance. 10000 0 FV= 10,000.00

Compute present value. % . PV= -9,050.63

To Press Display

Time-Value-of-Money and Amortization Worksheets 29

Example: Computing Present Value in Annuities

The Furros Company purchased equipment providing an annual savings

of $20,000 over 10 years. Assuming an annual discount rate of 10%, what

is the present value of the savings using an ordinary annuity and an

annuity due?

Cost Savings for a Present-Value Ordinary Annuity

Cost Savings for a Present-Value Annuity Due in a Leasing

Agreement

To Press Display

Set all variables to defaults. & } ! RST 0.00

Enter number of payments. 10 , N= 10.00

Enter interest rate per

payment period.

10 - I/Y= 10.00

Enter payment. 20000 S / PMT= -20,000.00

Answer: The present value of the savings is $122,891.34 with an ordinary

annuity and $135,180.48 with an annuity due.

Example: Computing Perpetual Annuities

To replace bricks in their highway system, the Land of Oz has issued

perpetual bonds paying $110 per $1000 bond. What price should you pay

for the bonds to earn 15% annually?

Answer: You should pay $733.33 for a perpetual ordinary annuity and

$843.33 for a perpetual annuity due.

A perpetual annuity can be an ordinary annuity or an annuity due

consisting of equal payments continuing indefinitely (for example, a

preferred stock yielding a constant dollar dividend).

Perpetual ordinary annuity

Compute present value

(ordinary annuity).

% . PV= 122,891.34

Set beginning-of-period

payments.

& ] & V BGN

Return to calculator mode. & U 0.00

Compute present value

(annuity due).

% . PV= 135,180.48

To Press Display

Calculate the present value for a

perpetual ordinary annuity.

110 6 15 2 N 733.33

Calculate the present value for a

perpetual annuity due.

H 110 N 843.33

To Press Display

Perpetual annuity due

Because the term (1 + I/Y / 100)-N in the present value annuity equations

approaches zero as N increases, you can use these equations to solve for

the present value of a perpetual annuity:

• Perpetual ordinary annuity

• Perpetual annuity due

Example: Computing Present Value of Variable

Cash Flows

The ABC Company purchased a machine that will save these end-of-year

amounts:

Year 1 2 3 4

Amount $5000 $7000 $8000 $10000

PV PMT

I/Y100

= ---------------------------

PV PMT PMT

I/Y⁄100 

= + ----------------------------

Given a 10% discount rate, does the present value of the cash flows

exceed the original cost of $23,000?

To Press Display

Set all variables to defaults. & }

!

RST 0.00

Enter interest rate per cash flow

period.

10 - I/Y= 10.00

Enter 1st cash flow. 5000 S 0 FV= -5,000.00

Enter 1st cash flow period. 1 , N= 1.00

Compute present value of 1st cash

flow.

% . PV= 4,545.45

Store in M1. D 1 4,545.45

Enter 2nd cash flow. 7000 S 0 FV= -7,000.00

Enter 2nd cash flow period. 2 , N= 2.00

Compute present value of 2nd

cash flow.

% . PV= 5,785.12

Sum to memory. D H 1 5,785.12

Enter 3rd cash flow. 8000 S 0 FV= -8,000.00

Enter period number. 3 , N= 3.00

Compute present value of 3rd

cash flow.

% . PV= 6,010.52

Sum to memory. D H 1 6,010.52

Enter 4th cash flow. 10000 S 0 FV= -10,000.00

Enter period number. 4 , N= 4.00

Time-Value-of-Money and Amortization Worksheets 33

Answer: The present value of the cash flows is $23,171.23, which exceeds

the machine’s cost by $171.23. This is a profitable investment.

Note: Although variable cash flow payments are not equal (unlike

annuity payments), you can solve for the present value by treating the

cash flows as a series of compound interest payments.

The present value of variable cash flows is the value of cash flows

occurring at the end of each payment period discounted back to the

beginning of the first cash flow period (time zero).

Example: Computing Present Value of a Lease