Question

Dolly has a cumulative time deposit account in a bank. She deposits Rs. 600 per month for 6 years. If at the end of the maturity period she gets Rs. 55026, find the rate of interest.

Answer 1

Step1:

Given data:

Amount received at the time of maturity$=\mathrm{Rs}.55026$

Instalment per month, $P=\mathrm{Rs}.600$

Number of years, $n=6$

Convert years into months.

$\begin{array}{rcl}n& =& 6years\\ & \Rightarrow & n=6\times 12\left(\because 1\mathrm{year}=12\mathrm{months}\right)\\ \therefore n& =& 72\\ \mathrm{So},n& =& 72\mathrm{months}\end{array}$

Step 2:

Calculate the Rate of interest:

$$\begin{gathered} \mathrm{Maturity}\mathrm{amount}=\left[1+\frac{(n+1)R}{2400}\right]\times n\times P \\ \Rightarrow 55026=\left[1+\frac{(72+1)R}{2400}\right]\times 72\times 600 \\ \Rightarrow 55026=\left[1+\frac{73R}{2400}\right]\times 72\times 600 \\ \Rightarrow 55026=\left[1+\frac{73R}{2400}\right]\times 43200 \\ \Rightarrow 55026=\left[\frac{2400+73R}{2400}\right]\times 43200 \\ \Rightarrow 55026=\left[2400+73R\right]\times 18 \\ \Rightarrow \frac{55026}{18}=2400+73R \\ \Rightarrow 3057=2400+73R \\ \Rightarrow 73R=3057-2400 \\ \Rightarrow 73R=657 \\ \Rightarrow R=\frac{657}{73} \\ \therefore R=9\% \end{gathered}$$

Hence, the rate of interest is $9\%$ p.a.