The certain sum amounts to Rs 9,982.50 in $ 2\frac12$ years at 12% p.a., interest compounded 10-monthly. The sum (in Rs) is:

Options
a) 8500
b) 7800
c) 8000
d) 7500

Solution

As per question
Interest rate per year = 12%
Interest rate to 10 months = $ \frac {10 \times 12}{12}$ = 10%
Time = $ 2 \frac12y$ = 30 months
Time = $ \frac {30}{10}$ = 3
A = $ p \frac{(1+r)}{100}^t$
9982.50 = $ p \frac{(1+10)}{100}^3$
9982.50 = $ p \frac{11}{10}^3$
9982.50 = $ p \times \frac{11}{10} \times \frac {11}{10} \times \frac{11}{10}$
P =$ 9982.50 \times \frac{1000}{1331}$
P = 7.50 x 1000
p = 7500

Ans: d) 7500