Question

Find the amount and the compound interest on Rs 10,000 for 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

P = Rs 10,000

Rate = 10% per annum = 5% per half year

n = years

There will be 3 half years inyears.

CI = A − P

= Rs 11576.25 − Rs 10000 = Rs 1,576.25

The amount for 1 year and 6 months can be calculated by first calculating the amount for 1 year using the compound interest formula, then calculating the simple interest for 6 months on the amount obtained at the end of 1 year.
The amount for the first year has to be calculated first.

$$\begin{gathered} \mathrm{A}=\mathrm{Rs}\left[10000{\left(1+\frac{10}{100}\right)}^1\right] \\ =\mathrm{Rs}\left[10000\left(\frac{11}{10}\right)\right] \\ =\mathrm{Rs}11000 \end{gathered}$$

By taking Rs 11,000 as the principle, the SI for the next $\frac{1}{2}$ year will be calculated.
$\mathrm{S}.\mathrm{I}.=\mathrm{Rs}\left(\frac{11000\times 10\times {\displaystyle \frac{1}{2}}}{100}\right)=\mathrm{Rs}550$

$\therefore$Interest for the first year =$\mathrm{Rs}11000-\mathrm{Rs}10000=\mathrm{Rs}1000$
$\therefore$Total compound interest $=\mathrm{Rs}1000+\mathrm{Rs}550=\mathrm{Rs}1550$

Therefore, the interest would be more when compounded half-yearly than the interest when compounded annually.