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- Quantitative Aptitude
6.Interest
medium
A man borrows ₹ $3825$ to be paid back with compound interest at the rate of $4 \%$ per annum by the end of $2$ years into equal yearly instalments. How much will be each instalment (In ₹) ?
A
$1275$
B
$1352$
C
$2028$
D
$2082$
Solution
Let each instalment be ₹ $x$.
$\therefore \quad \frac{x}{\left(1+\frac{4}{100}\right)^{2}}+\frac{x}{\left(1+\frac{4}{100}\right)}=3825$
i.e. $\quad \frac{x}{\left(\frac{26}{25}\right)^{2}}+\frac{x}{\left(\frac{26}{25}\right)}=3825$
$x+x \times \frac{26}{25}=3825 \times\left(\frac{26}{25}\right)^{2}$
i.e. $x \times \frac{51}{25}=3825 \times \frac{(26)^{2}}{(25)^{2}}$
$\begin{aligned}x &=3825 \times \frac{(26)^{2}}{(25)^{2}} \times \frac{25}{51} \\&=\frac{153 \times(26)^{2}}{51}=3 \times(26)^{2}=₹ 2028\end{aligned}$
Standard 13
Quantitative Aptitude
