Time Value of Money 49An Illustration
On December 31, you buy a car for Rs 200,000—paying 20 percent upfront and agreeing to pay the balance
in five equal annual installments. The rate of interest is 15 percent. Now:
Amount payable = 0.8 × 200000 = Rs 160000
PVAn= A[PVIFAr, n]
A= [160000 / 3352] = Rs 47732.70Sometimes annuities grow at a constant rate. Retirement and pension benefits, for example, increase
every year with a cost of living adjustment. The present value of a series of growing annuity can be estimated
using the following equation:
PV =
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎭
⎬
⎫
⎩
⎨
⎧
+
+
nrg
grA
1
) 1(
–
–
If A = Rs 6,600, r = 5 percent, n = 30 periods, g = 3.5 percent
PV = Rs 154,251
Loan Amortization
Consider an example similar to the above example. Assume that you have borrowed Rs10 lac from a financial
institution at an interest rate of 14 percent per annum. The loan is to be cleared in equal annual installments.
Annual installment = Rs 1000000/PVIFA (14, 5)
= Rs 1000000/3433 = Rs 291290This installment contains interest and principal components. The principal is retired partially every
year, and the interest is paid on the outstanding balance. The loan amortization schedule is presented in
Exhibit 2.5.
Exhibit 2.5 Loan amortization schedule
Annual Interest Principal Loan
Year installment (Rs) component (Rs) component (Rs) outstanding (Rs)
(1) (2) (3) (4) = (2) – (3) (5)
1 291,290 140,000 151,290* 1,000,000*
2 291,290 118,819 172,470* 848,710*
3 291,290 94,673 196,616* 676,239*
4 291,290 67,147 224,142* 479,622*
5 291,290 35,767 255,500* 255,480**These two figures do not coincide due to rounding off errors.
Working:
Interest for 1st year = 0.14 × 1000000 = Rs 140000
Principal component for 1st year = Annual installment – Interest for 1st year
= Rs 151290