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Question

Gopal has a cumulative deposit account and deposits Rs. $$900 $$per month for a period of $$4$$ years. If he gets Rs.$$ 52,020$$ at the time of maturity, find the rate of interest.


A
5%
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B
2%
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C
10%
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D
12%
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Solution

The correct option is C $$10\%$$
Installment per month $$\left( P \right) = Rs. 900$$
No. of months $$\left( n \right) = 4 \text{ years} = 12 \times 4 = 48 \text{ months}$$
Let rate of interest be $$r \%$$ per annum
$$t = \cfrac{n \left( n + 1 \right)}{2\times 12} = \cfrac{48 \times 49}{24} = 98$$
$$\therefore \; S.I. = P \times \cfrac{n \left( n + 1 \right)}{2\times 12} \times \cfrac{r}{100}$$
$$\Rightarrow \; S.I. = 900 \times \cfrac{48 \left( 48 + 1 \right)}{2\times 12} \times \cfrac{r}{100} = Rs. 882 r$$
Maturity value $$= Rs. \left(900 \times 48 + 882 r \right) = Rs \left( 43200 + 882 r \right)$$
maturity value $$= Rs. 52020$$
$$\therefore \; 43200 + 882 r = 52020$$
$$\Rightarrow \; 882 r = 52020 - 43200$$
$$\Rightarrow \; r = \cfrac{8820}{882} = 10 \%$$
Hence, rate of interest $$10 \%$$.

Mathematics

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