Find, to the nearest rupee, the amount and the compound interest on ₹ 9,000 for years at 8% per annum, the interest being compounded half-yearly.

Mathematics

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The interest being compounded half-yearly

P = ₹ 9,000, R = $\dfrac{8}{2}$ % = 4 %, T = $\dfrac{3}{2} \times 2$ = 3 years

A = P $\Big(1 + \dfrac{R}{100}\Big)^n$

= 9,000 x $\Big(1 + \dfrac{4}{100}\Big)^3$

= 9,000 x $(1 + 0.04)^3$

= 9,000 x $(1.04)^3$

= 9,000 x 1.12

= 10,123.77 ≈ 10,124

Compound Interest = Amount - Principal

= 10,123.77 - 9,000

= 1,123.77 ≈ 1,124

Hence, the amount = ₹ 10,124 and the compound interest = ₹ 1,124.

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