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Mathematics

Shahrukh opened a Recurring deposit account in a bank and deposited ₹ 800 per month for 1121\dfrac{1}{2} years. If he received ₹ 15084 at the time of maturity, find the rate of interest per annum.

Banking

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Answer

Let rate of interest be x%.

Given,

P = ₹ 800, n = (1 × 12 + 6) = 18 months, r = x%.

I = P×n(n+1)2×12×r100P \times \dfrac{n(n + 1)}{2 \times 12} \times \dfrac{r}{100}

∴I=₹800×18×192×12×x100=₹800×57x400=₹114x\therefore I = ₹ 800 \times \dfrac{18 \times 19}{2 \times 12} \times \dfrac{x}{100} \\[1em] = ₹ 800 \times \dfrac{57x}{400} \\[1em] = ₹ 114x

Sum deposited = ₹ 800 × 18 = ₹ 14400

Interest = Maturity value - Sum deposited

= ₹ 15084 - ₹ 14400 = ₹ 684.

⇒114x=684⇒x=684114⇒x=6%.\Rightarrow 114x = 684 \\[1em] \Rightarrow x = \dfrac{684}{114} \\[1em] \Rightarrow x = 6\%.

Hence, the rate of interest is 6% per annum.

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