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%
B
2%
C
10%
D
12%

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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