Question

A sum of Rs 25,000 is invested for 3 years at 20% per annum compound interest compounded annually. Calculate the interest for the third year.

Answer 1

Hint: Calculate the compound interest for the first year, then for the second year and finally for the third year. Since the interest is compounded annually, the interest at the end of each year will be added to the total amount over which the interest will be calculated for the next year. Use $S.I={\displaystyle \frac{P\times r\times t}{100}}$.

Complete step-by-step answer:

When interest on a certain sum is compounded annually, the interest at the end of each year is added to the total amount over which the interest is calculated for the next year.
Here we have for the first year P = 25,000, r = 20%,t =1 year.
Using $S.I={\displaystyle \frac{P\times r\times t}{100}}$, we get
Interest for the first year $={\displaystyle \frac{25000\times 20}{100}}=5000$
Hence P for second year = 25000+5000 = 30000, r= 20% and t = 1 year
Using $S.I={\displaystyle \frac{P\times r\times t}{100}}$, we get
Interest for the second year $={\displaystyle \frac{30000\times 20}{100}}=6000$
Hence P for third year = 30000+6000 = 36,000, r= 20% and t = 1year.
Using $S.I={\displaystyle \frac{P\times r\times t}{100}}$, we get
Interest for the third year $={\displaystyle \frac{36000\times 20\times 1}{100}}=7200$
Hence the interest for the third year = Rs 7200
Hence option [b] is correct.

Note: Alternatively we know for a sum compounded annually
$A_n=P{(1+{\displaystyle \frac{r}{100}})}^n$ and $I_n=A_n-A_{n-1}$ where $A_n$ is the amount at the end of the nth year and $I_n$is interest for the nth year.
Using, we get
$\begin{array}{rl}& I_3=P{(1+{\displaystyle \frac{r}{100}})}^3-P{(1+{\displaystyle \frac{r}{100}})}^2\\ & =25000{\left(1.2\right)}^3-25000{\left(1.2\right)}^2\\ & =43200-36000=7200\end{array}$
Hence interest for the third year = Rs 7200, which is same as obtained above.