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Mathematics

On a certain sum of money, let out at C.I., interests for first, second and third years are ₹ 1500; ₹ 1725 and ₹ 2070 respectively. Find the rate of interest for the (i) second year (ii) third year.

Compound Interest

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Answer

(i) Interest earned in first year = ₹ 1500

Interest earned in second year = ₹ 1725

Interest earned on ₹ 1500 in second year = Interest earned in second year - Interest earned in first year

= ₹ 1725 - ₹ 1500 = ₹ 225.

Rate of interest for second year

= Interest earned on ₹ 1500 in second yearInterest earned in first year×100=2251500×100\dfrac{\text{Interest earned on ₹ 1500 in second year}}{\text{Interest earned in first year}} \times 100 = \dfrac{225}{1500} \times 100 = 15%.

Hence, interest for the second year = 15%.

(ii) Interest earned in second year = ₹ 1725

Interest earned in third year = ₹ 2070

Interest earned on ₹ 1725 in third year = Interest earned in third year - Interest earned in second year

= ₹ 2070 - ₹ 1725 = ₹ 345.

Rate of interest for second year

= Interest earned on ₹ 1725 in third yearInterest earned in second year×100=3451725×100\dfrac{\text{Interest earned on ₹ 1725 in third year}}{\text{Interest earned in second year}} \times 100 = \dfrac{345}{1725} \times 100 = 20%.

Hence, interest for the third year = 20%.

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