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A invests Rs.1100 at a rate of interest 20% on simple interest for a certain period of time while B invests Rs.1000 at a rate of interest of 10% on compound interest for the same period of time. The difference between the interests earned by A and B is Rs.224.5. Find the time duration for which both invested their money. (compounded half-yearly)

A invests Rs.1100 at a rate of interest 20% on simple interest for a certain period of time while B invests Rs.1000 at a rate of interest of 10% on compound interest for the same period of time. The difference between the interests earned by A and B is Rs.224.5. Find the time duration for which both invested their money. (compounded half-yearly) Correct Answer 2

Formula:

Let P = Principle, R = rate of interest and N = time period

Simple interest = PNR/100

Compound interest (half yearly) = P(1 + (R/2)/100)2n - P

Calculation:

Let time period of which both invested their money be n.

Simple interest = 1100 × 20 × n/100 = Rs.220n

Compound interest = 1000(1 + 5/100)2n - 1000

⇒ 220n - 1000(1 + 5/100)2n + 1000 = 224.5

By using trial - error method,

⇒ n = 2

∴ For two years, both invested their money.

Important Points

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