A man borrows Rs. 5,000 at 12% p.a. compounded quarterly. He repays the loan in 2 years in two equal installments. What is the amount of each installment?

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Detailed Solution

Principal (P) = Rs. 5,000
Rate of interest (r) = 12% p.a.
Time period (t) = 2 years
Number of compounding periods (n) = 4 (compounded quarterly)

The amount after 2 years can be calculated using the following formula:

A = P * (1 + r/n)^(n*t)

A = 5000 * (1 + 0.12/4)^(4*2)
= Rs. 6,984.11

The amount of each installment can be calculated using the formula for the present value of an annuity:

PV = A * [1 - (1 + r/n)^(-n*t)] / (r/n)

PV = 6984.11 / 2
= Rs. 3,492.05

Using this value for PV, we can solve for A:

A = PV * (r/n) / [1 - (1 + r/n)^(-n*t)]

A = 3,492.05 * (0.12/4) / [1 - (1 + 0.12/4)^(-4*2)]
= Rs. 1,973.44

Therefore, the amount of each installment is Rs. 1,973.44.

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