ArithmeticWhat annual payment will discharge a debt of Rs.9760 due in 3 years at 25% per annum compound interest ?

What annual payment will discharge a debt of Rs.9760 due in 3 years at 25% per annum compound interest ?

A
5000
B
45000
C
5500
D
None

Solution:

Solution: Let the each installment be Rs ‘x’. Then

$\begin{array}{l} \Rightarrow \frac{x}{(1 + \frac{25}{100})} + \frac{x}{{(1 + \frac{25}{100})}^{2}} + \frac{x}{{(1 + \frac{25}{100})}^{3}} = 9760 \\ \Rightarrow \frac{x}{(\frac{5}{4})} + \frac{x}{{(\frac{5}{4})}^{2}} + \frac{x}{{(\frac{5}{4})}^{3}} = 9760 \\ \Rightarrow \frac{4 x}{5} + \frac{16 x}{25} + \frac{64 x}{125} = 9760 \\ \Rightarrow 100 x + 80 x + 64 x = 9760 \times 125 \\ x = \frac{9760 \times 125}{244} \\ x = 5000 \end{array}$