Question

Find the amount which Ram will get on $Rs.4096$, if he gave it for $18$ months at $12\frac{1}{2}\%$ per annum, interest being compounded half-yearly.

A: $Rs.4913$

B: $Rs.4425$

C: $Rs.4814$

D: $Rs.4124$

• A. $Rs.4913$
• B. $Rs.4425$
• C. $Rs.4814$
• D. $Rs.4124$

Answer 1

The correct option is A:

Here, Principal,P = $Rs.4096$

Time,t $=18$ months $=1\frac{1}{2}$ years

Rate $=12\frac{1}{2}\%=\frac{25}{2}\%$ per annum.

Here, the interest is compounded half yearly.

For half yearly, we have

Rate (compounded half-year) $=R=(\frac{25}{2}÷2)\%=\frac{25}{4}\%$

$n=1\frac{1}{2}\times 2=3$ (As interest is compounded half yearly)

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

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

$=4096(1+\frac{25}{400}{)}^3$

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

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

$=17\times 17\times 17$

$=4913$

Hence, Amount $=Rs.4913$