Question

Find the amount which Ram will get on $Rs.4,096$, he gave it for $18$ months at $12\frac{1}{2}\%$ per annum, interest being compounded half yearly.

Answer 1

Given;

$P=Rs.4,096$

$R=12\frac{1}{2}\%$ per annum.

$\Rightarrow R=\frac{25}{2}\%$ per annum.

$\Rightarrow R=\frac{1}{2}\times \frac{25}{2}\%$ per half yearly.

$\Rightarrow R=\frac{25}{4}\%$ per half yearly.--(1)

$T=18$ months

$T=\frac{18}{12}$ years

$T=1\frac{1}{2}$ years

$n=3$ half years---(2)

Now,

Total amount on compound interest half yearly is,

$A=P(1+\frac{R}{100}{)}^n$

$\Rightarrow A=4096(1+\frac{25}{4\times 100}{)}^3$

$\Rightarrow A=4096(1+\frac{1}{4\times 4}{)}^3$

$\Rightarrow A=4096(1+\frac{1}{16}{)}^3$

$\Rightarrow A=4096(\frac{17}{16}{)}^3$

$\Rightarrow A=4096\times \frac{17}{16}\times \frac{17}{16}\times \frac{17}{16}$

$\Rightarrow A=4096\times \frac{4913}{4096}$

$\Rightarrow A=4913$

Therefore, the required amount is $Rs.4913$.