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Mathematics

A certain money is deposited in a recurring deposit account for 15 months, If the interest earned for this deposit is one-fifth of the monthly instalment; the rate of interest is :

  1. 6%

  2. 2%

  3. 10%

  4. 4%

Banking

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Answer

Let money deposited per month be ₹ P.

Given,

Interest earned for this deposit is one-fifth of the monthly instalment.

Interest = 15×P=P5\dfrac{1}{5} \times P = \dfrac{P}{5}

Time (n) = 15 months

Let rate of interest be r%.

By formula,

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

Substituting values we get :

⇒P5=P×15×(15+1)2×12×r100⇒P5=P×15×16×r2×12×100⇒P5=P×240r2400⇒r=P×2400P×5×240⇒r=2%.\Rightarrow \dfrac{P}{5} = P \times \dfrac{15 \times (15 + 1)}{2 \times 12} \times \dfrac{r}{100} \\[1em] \Rightarrow \dfrac{P}{5} = P \times \dfrac{15 \times 16 \times r}{2 \times 12 \times 100} \\[1em] \Rightarrow \dfrac{P}{5} = P \times\dfrac{240r}{2400} \\[1em] \Rightarrow r = \dfrac{P \times 2400}{P \times 5 \times 240} \\[1em] \Rightarrow r = 2\%.

Hence, Option 2 is the correct option.

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