A loan of INR 19125 is to be paid back in two equal half yearly instalments. If the rate of interest is 8% p.a and the interest is compounded half yearly, then how much is each instalment (in INR)?Marks : 1Negative Marks : 0Answer here10155101251014010120
Question
A loan of INR 19125 is to be paid back in two equal half yearly instalments. If the rate of interest is 8% p.a and the interest is compounded half yearly, then how much is each instalment (in INR)?Marks : 1Negative Marks : 0Answer here10155101251014010120
Solution
To solve this problem, we need to use the formula for the present value of an annuity since the loan is being paid back in two equal installments. The formula is:
P = PMT * [(1 - (1 + r/n) ^ -nt) / (r/n)]
Where: P = present value (the loan amount) PMT = payment amount per period (what we're trying to find) r = annual interest rate (in decimal form) n = number of compounding periods per year t = number of years
Given: P = INR 19125 r = 8% per annum = 0.08 n = 2 (since interest is compounded half yearly) t = 1 (since the loan is to be paid back in two half yearly installments, i.e., within one year)
We need to rearrange the formula to solve for PMT:
PMT = P * (r/n) / [(1 - (1 + r/n) ^ -nt)]
Substituting the given values:
PMT = 19125 * (0.08/2) / [1 - (1 + 0.08/2) ^ -(2*1)]
Solving this will give us the value of each installment.
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