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Ajit borrowed Rs. 63000 from a bank at a rate of 10% p.a., interest being compounded annually. He repaid the sum in two equal installments, the first after one year and the second after another year. He then invested a sum equal to his installment at an interest of 15% for two years compounded annually. What is the interest he has earned?

Ajit borrowed Rs. 63000 from a bank at a rate of 10% p.a., interest being compounded annually. He repaid the sum in two equal installments, the first after one year and the second after another year. He then invested a sum equal to his installment at an interest of 15% for two years compounded annually. What is the interest he has earned? Correct Answer Rs. 11706.75

We know that

P = x / ((1 + r / 100)) + x / (1 + r / 100)2 + x / (1 + r / 100)3 + ……. x / (1 + r / 100)n

Where P is the principal, r is the rate of interest, x is value of each installment, n is the number of years

According to the question loan is taken for 2 years

So,

⇒ 63000 = x / ((1 + 10 / 100)) + x / (1 + 10 / 100)2

⇒ 63000 = 10x / 11 + 100x / 121

⇒ 63000 = (110x + 100x) / 121

⇒ 63000 = 210x / 121

⇒ x = 36300

Now, he invested Rs 36300 at the rate of 15% compound interest for 2 years

⇒ A = 36300 (1 + 15 / 100)2

⇒ A = 48006.75

∴ required Interest = 48006.75 - 36300 = Rs. 11706.75

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