Question

A person gifted Rs. 2500 to his two children aged 10 years and 15 years respectively with the condition that the sum should be divided in such a way that the two children got the same amount when they reached the age of 30 years. Assuming that the rate of compound interest charged is 5% p.a., what is the value of gift received by each child?

Answer 1

Use the Compound Interest Formula

$$A=P(1+\dfrac{r}{n})^{nt}$$

Given $r=0.05, n=1$

$$P_1(1+\dfrac{0.05}{1})^{1(30-10)}=P_2(1+\dfrac{0.05}{1})^{1(30-15)}$$

$$P_2=P_1(1.05)^5$$

$$P_1+P_2=2500$$

Substitute

$$P_1+P_1(1.05)^5=2500$$

$$P_1=\dfrac{2500}{1+(1.05)^5}$$

$$P_1=\dfrac{2500}{1+(1.05)^5}$$

$$P_1=1098.28$$

$$P_2=1401.72$$

The children aged 10 years receives Rs.1098.28 and the children aged 15 years receives Rs.1401.72.