Test Index

Time Value of Money

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Question : 75 of 99

Marks: +1, -0

An overdraft of Rs. 50,000 to be paid back in equal annual installments over a period of 20 years. Find the value of Installment, if interest is compounded annually at

14\%

per annum. [Given

(1.14)^{20}=13.74349]

Rs.7550.50
Rs.7549.30
Rs.7559.50
Rs.7560.50

Solution:

Concept:

Loan repayment using equal annual installments follows the present value of annuity formula.

Explanation:

Given: Overdraft (loan)

PV = 50000

, interest rate

r = 14\% = 0.14

, time

n = 20

years.

The present value of an annuity formula is:

PV = PMT \times \frac{1 - (1+r)^{-n}}{r}

We are given

(1.14)^{20} = 13.74349

, so

(1.14)^{-20} = \frac{1}{13.74349} \approx 0.07276

.

Then

\frac{1 - (1+r)^{-n}}{r} = \frac{1 - 0.07276}{0.14} = \frac{0.92724}{0.14} = 6.62314

.

Therefore,

PMT = \frac{PV}{6.62314} = \frac{50000}{6.62314} \approx 7549.30

.

Answer:

Rs. 7549.30

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