With Residual Value

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The Peach Bright Company wants to purchase a machine currently leased

from your company. You offer to sell it for the present value of the lease

discounted at an annual interest rate of 22% compounded monthly. The

machine has a residual value of $6500 with 46 monthly payments of

$1200 remaining on the lease. If the payments are due at the beginning

of each month, how much should you charge for the machine?

Compute present value of 4th

cash flow.

% . PV= 6,830.13

Sum to memory. D H 1 6,830.13

Recall total present value. J 1 23,171.23

Subtract original cost. B 23000 N 171.23

To Press Display

The total value of the machine is the present value of the residual value

plus the present value of the lease payments.

Answer: Peach Bright should pay your company $40,573.18 for the

machine.

Example: Computing Other Monthly Payments

If you finance the purchase of a new desk and chair for $525 at 20% APR

compounded monthly for two years, how much is the monthly payment?

To Press Display

Set all variables to defaults. & } ! RST 0.00

Set beginning-of-period

payments.

& ] & V BGN

Return to standard-calculator

mode.

& U 0.00

Enter number of payments. 46 , N= 46.00

Calculate and enter periodic

interest rate.

22 6 12 N - I/Y= 1.83

Enter residual value of asset. 6500 S 0 FV= -6,500.00

Compute residual present value. % . PV= 2,818.22

Enter lease payment amount. 1200 S / PMT= -1,200.00

Compute present value of lease

payments.

% . PV= 40,573.18

To Press Display

Set all variables to defaults. & } ! RST 0.00

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

Time-Value-of-Money and Amortization Worksheets 35

Answer: Your monthly payment is $26.72.

Example: Saving With Monthly Deposits

Note: Accounts with payments made at the beginning of the period are

referred to as annuity due accounts. Interest begins accumulating earlier

and produces slightly higher yields.

You invest $200 at the beginning of each month in a retirement plan.

What will the account balance be at the end of 20 years, if the fund earns

an annual interest of 7.5 % compounded monthly, assuming beginningof-

period payments?

Return to standard-calculator

mode

& U 0.00

Enter number of payments using

payment multiplier.

2 & Z , N= 24.00

Enter interest rate. 20 - I/Y= 20.00

Enter loan amount. 525 . PV= 525.00

Compute payment. % / PMT= -26.72

To Press Display

Set all variables to defaults. & } ! RST 0.00

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

Set beginning-of-period

payments.

& ] & V BGN

Return to standard-calculator

mode.

& U 0.00

To Press Display

Answer: Depositing $200 at the beginning of each month for 20 years

results in a future amount of $111,438.31.

Example: Computing Amount to Borrow and

The Peach Bright Company wants to purchase a machine currently leased

from your company. You offer to sell it for the present value of the lease

discounted at an annual interest rate of 22% compounded monthly. The

machine has a residual value of $6500 with 46 monthly payments of

$1200 remaining on the lease. If the payments are due at the beginning

of each month, how much should you charge for the machine?

Compute present value of 4th

cash flow.

% . PV= 6,830.13

Sum to memory. D H 1 6,830.13

Recall total present value. J 1 23,171.23

Subtract original cost. B 23000 N 171.23

To Press Display

The total value of the machine is the present value of the residual value

plus the present value of the lease payments.

Answer: Peach Bright should pay your company $40,573.18 for the

machine.

Example: Computing Other Monthly Payments

If you finance the purchase of a new desk and chair for $525 at 20% APR

compounded monthly for two years, how much is the monthly payment?

To Press Display

Set all variables to defaults. & } ! RST 0.00

Set beginning-of-period

payments.

& ] & V BGN

Return to standard-calculator

mode.

& U 0.00

Enter number of payments. 46 , N= 46.00

Calculate and enter periodic

interest rate.

22 6 12 N - I/Y= 1.83

Enter residual value of asset. 6500 S 0 FV= -6,500.00

Compute residual present value. % . PV= 2,818.22

Enter lease payment amount. 1200 S / PMT= -1,200.00

Compute present value of lease

payments.

% . PV= 40,573.18

To Press Display

Set all variables to defaults. & } ! RST 0.00

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

Time-Value-of-Money and Amortization Worksheets 35

Answer: Your monthly payment is $26.72.

Example: Saving With Monthly Deposits

Note: Accounts with payments made at the beginning of the period are

referred to as annuity due accounts. Interest begins accumulating earlier

and produces slightly higher yields.

You invest $200 at the beginning of each month in a retirement plan.

What will the account balance be at the end of 20 years, if the fund earns

an annual interest of 7.5 % compounded monthly, assuming beginningof-

period payments?

Return to standard-calculator

mode

& U 0.00

Enter number of payments using

payment multiplier.

2 & Z , N= 24.00

Enter interest rate. 20 - I/Y= 20.00

Enter loan amount. 525 . PV= 525.00

Compute payment. % / PMT= -26.72

To Press Display

Set all variables to defaults. & } ! RST 0.00

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

Set beginning-of-period

payments.

& ] & V BGN

Return to standard-calculator

mode.

& U 0.00

To Press Display

Answer: Depositing $200 at the beginning of each month for 20 years

results in a future amount of $111,438.31.

Example: Computing Amount to Borrow and