Question

Calculate the amount and compound interest on $Rs18,000$ for $2\frac{1}{2}$ years at $10\%$ per annum compounded annually.

Answer 1

Here, the principal amount is $P=18000$, time is $2\frac{1}{2}$ and rate of interest is $10$% and we know that the formula to calculate amount is $A=P{[1+\frac{R}{100}]}^n$, so let us first calculate the amount for $2$ years as follows:

$A=P{[1+\frac{R}{100}]}^n$

$=18000{[1+\frac{10}{100}]}^2$

$=18000{[1+\frac{1}{10}]}^2$

$=18000{\left[\frac{11}{10}\right]}^2$

$=18000\times \frac{11}{10}\times \frac{11}{10}$

$=21780$

Thus, the amount is Rs. $21780$

Now, to find the compound interest for $2$ years, we subtract the principal amount from the total amount as shown below:

$C.I=21780-18000=3780$

Now let us find the half-year compound interest by using the Simple Interest Formula :

i.e $S.I.=\frac{P\times R\times T}{100}$

$\Rightarrow S.I.=21780\times \frac{10}{100}\times \frac{1}{2}$

$=\frac{21780}{20}$

$=1089$

Total compound interest after $2.5$ years is $3780+1089=Rs4869$.

And, the amount $=P+I$

$=18000+4869$

$=Rs22869$