What annual payment (In ₹) will discharge a debt of ₹ 1025 due in 2 years at rate of 5 % compoun

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6.Interest

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What annual payment (In ₹) will discharge a debt of ₹ $1025$ due in $2$ years at the rate of $5 \%$ compound interest?

A

$550$

B

$551.25$

C

$560$

D

$560.75$

Solution

Let each annual instalment be ₹ $x$.

$\therefore \quad \frac{x}{\left(1+\frac{5}{100}\right)^{2}}+\frac{x}{\left(1+\frac{5}{100}\right)}=1025$

or $x \times\left(\frac{20}{21}\right)^{2}+x\left(\frac{20}{21}\right)=1025$

Or

$\frac{400 x}{441}+\frac{20 x}{21}=1025$

$\Rightarrow$

$\frac{400 x+420 x}{441}=1025$

or $x=\frac{1025 \times 441}{820}=₹ 551.25$

Hence each annual instalment $=₹ 551.25$

Standard 13

Quantitative Aptitude

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