A sum of money amounts to Rs 10240 in 2 years

Question:

A sum of money amounts to Rs 10240 in 2 years at $6 \frac{2}{3} \%$ per annum, compounded annually. Find the sum.

Solution:

Let $P$ be the sum.

Rate of interest, $R=6 \frac{2}{3} \%=\frac{20}{3} \%$

Time, $n=2$ years

Now, $A=P \times\left(1+\frac{20}{100 \times 3}\right)^{2}$

$=$ Rs. $P \times\left(1+\frac{20}{300}\right)^{2}$

$=$ Rs. $P \times\left(\frac{300+20}{300}\right)^{2}$

$=$ Rs. $P \times\left(\frac{320}{300}\right)^{2}$

$=$ Rs. $P \times\left(\frac{16}{15} \times \frac{16}{15}\right)$

$=$ Rs. $\frac{256 P}{225}$

$\Rightarrow$ Rs. $10240=$ Rs. $\frac{256 P}{225}$

$\Rightarrow$ Rs. $\left(\frac{10240 \times 225}{256}\right)=P$

$\therefore P=$ Rs. 9000

Hence, the required sum is Rs. 9000

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