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Equal amount invested by Sachin and Yogesh in the test book for 3 years. Sachin invested compound interest at a rate of 10% per annum for three years and Yogesh invested simple interest at a rate of 10% per annum for 1st two years and rate of interest changes for 3rd year. If the return on investment is equal for Sachin and Yogesh, then what will be the the Rate of interest for Sachin in 3rd year?

Equal amount invested by Sachin and Yogesh in the test book for 3 years. Sachin invested compound interest at a rate of 10% per annum for three years and Yogesh invested simple interest at a rate of 10% per annum for 1st two years and rate of interest changes for 3rd year. If the return on investment is equal for Sachin and Yogesh, then what will be the the Rate of interest for Sachin in 3rd year? Correct Answer 13.1%

Given:

Sachin invested = compound interest at a rate of 10% per annum for three years

Yogesh invested = simple interest at a rate of 10% per annum for 1st two years and rate of interest changes for 3rd year.

Formula used:

Simple interest = (Principal × rate × time)/100

Compound interest = principle × (1 + r/100) time

Calculations:

Let the initial amount be x.

Sachin amount at the end of 3rd year = x (1 + 10/100)3 = x (11/10)3 = 1331P/1000

Let the rate of interest for 3rd year be R. Then Yogesh amount at the end of 3rd year

⇒ (P × 10 × 2)/100 + (P × 1 × R)/100 + p

⇒ p/5 + PR/100 + P

Sachin return = Yogesh return

⇒ 1331P/1000 = p/5 +PR/100 + p

⇒ 1331P/1000 – 6/5P = PR/100

⇒ 1331/1000 – 6/5 = R/100

⇒ R = 655/1000 × 100

∴ R = 13.1%

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