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Mathematics

If the interest is compounded half-yearly, calculate the amount when principal is ₹ 7400; the rate of interest is 5% per annum and the duration is one year.

Compound Interest

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Answer

Given,

P = ₹ 7400

r = 5% compounded half-yearly

n = 1 year

When rate of interest is compounded half-yearly,

A = P(1+r2×100)n×2P\Big(1 + \dfrac{r}{2 \times 100}\Big)^{n \times 2}

Substituting values we get :

A=7400×(1+52×100)1×2=7400×(1+140)2=7400×(4140)2=7400×16811600=₹7774.63A = 7400 \times \Big(1 + \dfrac{5}{2 \times 100}\Big)^{1 \times 2} \\[1em] = 7400 \times \Big(1 + \dfrac{1}{40}\Big)^2 \\[1em] = 7400 \times \Big(\dfrac{41}{40}\Big)^2 \\[1em] = 7400 \times \dfrac{1681}{1600} \\[1em] = ₹ 7774.63

Hence, amount = ₹ 7774.63

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