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