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Mathematics

₹ 800 per month is deposited in an R.D. account for one and half years. If the depositor gets ₹ 2,280 as interest at the time of maturity, the rate of interest is :

  1. 20%

  2. 15%

  3. 10%

  4. 12%

Banking

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Answer

Given,

Deposit per month (P) = ₹ 800

Time (n) = 18 months (or 1.5 years)

Interest = 2280

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 :

⇒2280=800×18×(18+1)2×12×r100⇒2280=800×18×1924×r100⇒2280=6×19×r⇒r=22806×19⇒r=2280114⇒r=20%.\Rightarrow 2280 = 800 \times \dfrac{18 \times (18 + 1)}{2 \times 12} \times \dfrac{r}{100} \\[1em] \Rightarrow 2280 = 800 \times \dfrac{18 \times 19}{24} \times \dfrac{r}{100} \\[1em] \Rightarrow 2280 = 6 \times 19 \times r \\[1em] \Rightarrow r = \dfrac{2280}{6 \times 19} \\[1em] \Rightarrow r = \dfrac{2280}{114} \\[1em] \Rightarrow r = 20\%.

Hence, Option 1 is the correct option.

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