ArithmeticA sum of money is borrowed and paid back in two annual installments of Rs.500 each allowing 10% compound interest. The sum borrowed was (approximately)

A sum of money is borrowed and paid back in two annual installments of Rs.500 each allowing 10% compound interest. The sum borrowed was (approximately)

A
950
B
868
C
715
D
855

Solution:

Solution: Present worth of Rs x due T years $= \frac{x}{{(1 + \frac{R}{100})}^{T}}$

Principal = Present worth of Rs.500 due 1 year +

Present worth of Rs.500 due to 2 years

$\begin{array}{l} = \frac{500}{{(1 + \frac{10}{100})}^{1}} + \frac{500}{{(1 + \frac{10}{100})}^{2}} \\ = 454.54 + 413.22 \\ = 868 \end{array}$