Question

Find the amount and the compound Interest when the interest is compounded annually
[i] Principal = INR 4000, rate = 10 % per annum and time = 2 years
[ii] Principal = INR 4000, rate = 15.5 % per annum and time = 2 years

Answer 1

Hint: Use the fact that when interest is compounded annually, interest is calculated on the previous year amount and the interest of the previous year. In other words, it is equivalent to reinvesting the interest instead of paying it. Hence, calculate the interest for the first year and hence the amount on which interest is levied on in the second year. Finally, calculate the interest for the second year and hence the total amount. Alternatively use $\text{A=}P{{\left( 1+\dfrac{r}{100} \right)}^{n}}$.

Complete step-by-step solution:

[i] We have P = INR 4000, t = 2 years and r = 10% p.a
Interest for the first year $=\dfrac{P\times r\times 1}{100}=\dfrac{4000\times 10}{100}=400$
Hence for the second year, we have P = 4000+400 = INR 4400, r = 10% p.a
Interest for the second year $=\dfrac{P\times r\times 1}{100}=\dfrac{4400\times 10}{100}=440$
Hence we have amount = 4400+440 = INR 4840 and Compound Interest = 4840 – 4000 = INR 840.
[ii] We have P = INR 4000, t = 2years and r = 15.5% p.a
Interest for the first year $=\dfrac{P\times r\times 1}{100}=\dfrac{4000\times 15.5}{100}=620$
Hence for the second year, we have P = 4000+620 = INR 4620, r = 15.5% p.a
Interest for the second year $=\dfrac{P\times r\times 1}{100}=\dfrac{4620\times 15.5}{100}=716.10$
Hence we have amount = 4620+716.10 = INR 5336.10 and Compound Interest = 5336.10 – 4000 = INR 1336.10.

Note: Alternative solution:
We know that $\text{A=P}{{\left( 1+\dfrac{r}{100} \right)}^{n}}$
[i] We have P = INR 4000, t = 2years and r = 10% p.a
Hence we have $A=4000{{\left( 1+\dfrac{10}{100} \right)}^{2}}=4000\times {{1.1}^{2}}=4840$
Hence amount = INR 4840 and Compound Interest = 4840-4000 = INR 840.
[ii] We have P = INR 4000, t = 2years and r = 15.5% p.a
Hence we have $A=4000{{\left( 1+\dfrac{15.5}{100} \right)}^{2}}=4000\times {{1.155}^{2}}=5336.10$
Hence amount = INR 5336.10 and Compound Interest = 5336.10 – 4000 = INR 1336.10.