A man borrows Rs. 50,000 at 14% per annum compounded half-yearly. He agrees to repay the loan in 3 equal annual installments. Find the value of each installment.

Interest rate = 14% p.a. compounded half-yearly Time period = 3 years Number of half-years = 6 (2 half-years in 1 year)

Amount = P(1 + (r/n))^(nt) = 50000(1 + (0.14/2))^(2*3) = 50000(1.07)^6 = Rs. 76,799.39

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 = 76799.39*(1 - (1 + 0.07)^-3)/0.07 = Rs. 28,225.63

Therefore, the value of each installment is Rs. 28,225.63.