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Mathematics

The maturity value of a recurring deposit account is ₹ 42,400. If the account is held for 2 years and the rate of interest is 10% per annum, find the amount of each monthly installment.

Banking

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Answer

Let monthly installment be ₹ P.

Given,

Time (n) = 2 years = 24 months.

Rate (r) = 10%.

Maturity value = ₹ 42400.

By formula,

Maturity value = P × n + P × n(n+1)2×12×r100\dfrac{n(n + 1)}{2 \times 12} \times \dfrac{r}{100}

Substituting values we get :

⇒42400=P×24+P×24×252×12×10100⇒42400=24P+P×25×110⇒42400=24P+2.5P⇒26.5P=42400⇒P=4240026.5⇒P=1600.\Rightarrow 42400 = P \times 24 + P \times \dfrac{24 \times 25}{2 \times 12} \times \dfrac{10}{100} \\[1em] \Rightarrow 42400 = 24P + P \times 25 \times \dfrac{1}{10} \\[1em] \Rightarrow 42400 = 24P + 2.5P \\[1em] \Rightarrow 26.5P = 42400 \\[1em] \Rightarrow P = \dfrac{42400}{26.5} \\[1em] \Rightarrow P = 1600.

Hence, monthly installment = ₹ 1600.

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