Question

A sum of ₹ 9600 is invested for 3 years at 10% per annum at compound interest.
(i) What is the sum due at the end of the first year?
(ii) What is the sum due at the end of the second year?
(iii) Find the compound interest earned in 2 years.
(iv) Find the difference between the answers in (ii) and (i) and find the interest on this sum for one year.
(v) Hence, write down the compound interest for the third year.

Answer 1

It is given that
Principal = ₹ 9600
Rate of interest = 10% p.a.
Period = 3 years
We know that
Interest for the first year = $\frac{Prt}{100}$
Substituting the values = (9600 × 10 × 1)/ 100 = ₹ 960

(i) Amount after one year = 9600 – 960 = ₹ 10560
So the principal for the second year = ₹ 10560
Here the interest for the second year = (10560 × 10 × 1)/ 100
= ₹ 1056

(ii) Amount after two years = 10560 + 1056 = ₹ 11616

(iii) Compound interest earned in 2 years = 960 + 10560 = ₹2016

(iv) Difference between the answers in (ii) and (i) = 11616 – 10560 = ₹ 1056
We know that
Interest on ₹ 1056 for 1 year at the rate of 10% p.a.
= (1056 × 10 × 1)/ 100 = ₹ 105.60

(v) Here
Principal for the third year = ₹ 11616
So the interest for the third year = (11616 × 10 × 1)/ 100 = ₹1161.60