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Q.

A person borrows Rs. 20,000 at 12% per annum compounded quarterly. He agrees to repay the loan in 2 equal annual installments. Find the value of each installment. ( Report the value nearest to thousands)

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a

15000

b

5000

c

10000

d

24000

answer is C.

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Detailed Solution

Interest rate = 12% p.a. compounded quarterly
Time period = 2 years
Number of quarters = 8 (4 quarters in 1 year)

Amount = P(1 + (r/n))^(nt)
= 20000(1 + (0.12/4))^(4*2)
= 20000(1.03)^8
= Rs. 29,137.62

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

PMT = A*(1 - (1 + r)^-n)/r

where PMT is the installment amount, A is the total amount borrowed, r is the interest rate per installment period, and n is the total number of installments.

PMT = 29137.62*(1 - (1 + 0.03)^-2)/0.03
= Rs. 15,139.69 (approx)

Therefore, the value of each installment is Rs. 15,139.69.

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