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Mathematics

Joseph has a recurring deposit account in a bank for 3 years at 10% p.a. simple interest. If he gets ₹ 16,650 as interest at the time of maturity, find his monthly deposit and the maturity value.

Banking

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Answer

Let monthly deposit be ₹ P.

Given,

r = 10%

n = 3 years or 36 months

I = ₹ 16,650

By formula,

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

Substituting values we get :

⇒16650=P×36×(36+1)2×12×10100⇒16650=P×36×3724×110⇒16650=P×3×3720⇒P=16650×20111⇒P=333000111=₹ 3000.\Rightarrow 16650 = P \times \dfrac{36 \times (36 + 1)}{2 \times 12} \times \dfrac{10}{100} \\[1em] \Rightarrow 16650 = P \times \dfrac{36 \times 37}{24} \times \dfrac{1}{10} \\[1em] \Rightarrow 16650 = P \times \dfrac{3 \times 37}{20} \\[1em] \Rightarrow P = \dfrac{16650 \times 20}{111} \\[1em] \Rightarrow P = \dfrac{333000}{111} = \text{₹ 3000}.

Sum deposited = ₹ 3,000 × 36 = ₹ 1,08,000.

M.V. = Sum deposited + Interest = ₹ 1,08,000 + ₹ 16,650 = ₹ 1,24,650.

Hence, maturity value = ₹ 1,24,650.

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