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Mathematics

Simple interest on a sum of money for 2 years at 4% growth rate is ₹ 450. Find compound interest on the same sum and at the same rate for 1 year, if the interest is reckoned half-yearly.

Compound Interest

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Answer

Let sum of money be ₹ x.

Given,

Simple interest on sum of money for 2 years at 4% growth rate is ₹ 450.

By formula,

S.I.=P×R×T100⇒450=x×4×2100⇒x=450×1004×2⇒x=₹5625.S.I. = \dfrac{P \times R \times T}{100} \\[1em] \Rightarrow 450 = \dfrac{x \times 4 \times 2}{100} \\[1em] \Rightarrow x = \dfrac{450 \times 100}{4 \times 2} \\[1em] \Rightarrow x = ₹ 5625.

For C.I. :

P = ₹ 5625

n = 1 year

r = 4% compounded half-yearly

A=P(1+r2×100)n×2=5625×(1+4200)1×2=5625×(204200)2=5625×(5150)2=5625×26012500=₹5852.25A = P\Big(1 + \dfrac{r}{2 \times 100}\Big)^{n \times 2} \\[1em] = 5625 \times \Big(1 + \dfrac{4}{200}\Big)^{1 \times 2} \\[1em] = 5625 \times \Big(\dfrac{204}{200}\Big)^2 \\[1em] = 5625 \times \Big(\dfrac{51}{50}\Big)^2 \\[1em] = 5625 \times \dfrac{2601}{2500} \\[1em] = ₹ 5852.25

C.I. = A - P = ₹ 5852.25 - ₹ 5625 = ₹ 227.25

Hence, compound interest = ₹ 227.25

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