Question

Find the amount and the compound interest on INR $10,000$ for $1\frac{1}{2}$ years at $10\%$ per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?

Answer 1

Principal $=10,000$

Rate $=10\%$ per annum $=5\%$ half-yearly

Time $=1\frac{1}{2}\text{years}=\frac{3}{2}\times 2=3$ compounded half-yearly

We know that,

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

$\Rightarrow A=10000{\left(1+\frac{10}{100\times 2}\right)}^3$

$=10000{\left(\frac{21}{20}\right)}^3$

$=\frac{9261}{8000}\times 10000$

$=11567.25$

Interest $=11567.25-10000$

$=1576.25$

If compounded yearly Amount at $1^{st}$ year $=10000{\left(1+\frac{10}{100}\right)}^1$

$=11000$

Interest for half year $=\frac{PRT}{100}=\frac{11000\times 10\times 1}{100\times 2}$

$=550$

Total interest when compounded Annually $=\left(11000-10000\right)+550$

$=1000+550=1550$

Thus, the interest is maximum when compounded half-yearly.