Time Line:
06%1 2 3
1,000 PMT PMT PMT
Equation:
The same general equation used to find the PV of an ordinary annuity is shown below:
(2-5)
.
- NUMERICAL SOLUTION
We know the PV, the interest rate, and the number of periods. The only unknown
variable is the payment:
(2-5a)
Using Equation 2-5a, we can solve the equation for the payment:
PMT$1,000/2.6730$374.11.
$1,000PMT
°
1
1
(10.06)^3
0.06
¢
PMT(2.6730)
PMT
°
1
1
(10.06)^3
0.06
¢
.
$1,000PMT a
3
t 1
a
1
1 0.06
b
t
PMT(PVIFAi,n)
PMT°
1
1
(1i)n
i
¢
PMT a
n
t 1
a
1
1 i
b
t
PVAn PMTa
1
1 i
b
1
PMTa
1
1 i
b
2
PMTa
1
1 i
b
n
Amortized Loans 89
TABLE 2-2 Loan Amortization Schedule, 6 Percent Interest Rate
Beginning Repayment Remaining
Amount Payment Interesta of Principalb Balance
Year (1) (2) (3) (2) (3) (4) (1) (4) (5)
1 $1,000.00 $ 374.11 $ 60.00 $ 314.11 $685.89
2 685.89 374.11 41.15 332.96 352.93
3 352.93 374.11 21.18 352.93 0.00
$1,122.33 $122.33 $1,000.00
aInterest is calculated by multiplying the loan balance at the beginning of the year by the interest rate. Therefore,
interest in Year 1 is $1,000(0.06) $60; in Year 2 it is $685.89(0.06) $41.15; and in Year 3 it is $352.93(0.06)
$21.18.b
Repayment of principal is equal to the payment of $374.11 minus the interest charge for each year.
Time Value of Money 87
