Question

Difference between CI received in the first 1.5 years (compounded annually) at 20% per annum and CI received in the last 1.5 years when compounded half-yearly at the same rate of interest on the same sum is Rs 715. Find the sum.​

Answer 1

Rs 43423.17

Explanation:

You want the sum invested at 20% for 1.5 years when the difference in interest received between half-yearly compounding and annual compounding is Rs 715.

Compound interest

The account value for an account earning compound interest is given by ...

A = P(1 +r/n)^(nt)

for principal P invested at annual rate r compounded n times per year for t years.

Difference

The difference in the two account values is ...

∆A = P(1 +0.20/2)^(2·1.5) -P(1 +0.20)^1.5

Solving for P, we have ...

P = 715/(1.10^3 -1.20^1.5) ≈ 43423.17

The sum invested is Rs 43423.17.

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