Question

Find the compound interest on Rs.8000 for $1\frac{1}{2}$ years at 10% per annum interest being payable half yearly-

Answer 1

Given that, principal amount $=Rs.8000$, rate of interest $=10\%$ per annum, time$=1\frac{1}{2}$ years.

Also, given that the interest is compounded half yearly.

So, rate of interest $=5\%$ per half year

and time $=1\frac{1}{2}$ years $=3$ half years

We know that, $\text{simple interest}=\frac{P\times R\times T}{100}$

So, interest for the first half year $=Rs.\left[\frac{8000\times 5\times 1}{100}\right]$

$=Rs.400$

Now, amount at the end of the first half year $=Rs.8000+Rs.400$

$=Rs.8400$

So, principal for the second half year $=Rs.8400$

So, interest for the second half year $=Rs.\left[\frac{8400\times 5\times 1}{100}\right]$

$=Rs.420$

So, amount at the end of the second half year $=Rs.8400+Rs.420$

$=Rs.8820$

So, principal for the third half year $=Rs.8820$

So, interest for the third half year $=Rs.\left[\frac{8820\times 5\times 1}{100}\right]$

$=Rs.441$

So, amount at the end of third half year $=Rs.8820+Rs.441=Rs.9261$

$\therefore$ Compound interest $=Rs.9261-Rs.8000=Rs.1261$

Hence, the compound interest on $Rs.8000$ at $10\%$ per annum for $1\frac{1}{2}$ years, compounded half yearly, is $Rs.1261$.