Question

What annual payment will discharge a debt of Rs. $1025$ due in $2$ years at the rate of $5\%$ compound interest?

• A. Rs. $550$
• B. Rs. $551.25$
• C. Rs. $560$
• D. Rs. $560.75$

Answer 1

The correct option is B Rs. $551.25$

Let each instalment be $x$. Then,
(Present worth of $x$ due $1$ year hence) $+$(Present worth of $x$ due $2$ years hence)$=1025$
$\frac{x}{1+\frac{5}{100}}+\frac{x}{1+{\left(\frac{5}{100}\right)}^2}=1025$
$\frac{20x}{21}+\frac{400x}{441}=1025$
$820x=1025\times 441$
$x=551.25$
So, value of each instalment $=$ Rs. $551.25$.
Answer $\left(B\right)$ Rs. $551.25$