Question

A bank pays 6 % interest compounded quarterly . What equal deposits have to be made at the end of each quarter for 3 years if you want to have Rs 1500 at the end of 3 years?

• A. 139.36
• B. 116.58
• C. 234
• D. 435

Answer 1

The correct option is B 116.58

Let R be deposited in the bank at end of

each quarter for 3 years accumulate Rs. 1500 at

6% per annum.

$\therefore$ we have $S=RS1500$

$n=$ number of periods $=3\times 4=12$ quarter

$i=$ interest on Rs. per period

$=\frac{6}{100\times 4}=\frac{6}{400}=0.015$

Using the formula,

$S=R\left[\frac{(1+i{)}^n-1}{i}\right],$ we have

$1500=R\left[\frac{(1+0.015{)}^{12}-1}{0.015}\right]...\left(1\right)$

Let $x=(0.015{)}^{12}$

$logx=log(0.015{)}^{12}$

$logx=12\times log\left(0.015\right)$

$=12\times \left(0.0064\right)$

$=0.0768$

$x=$ antilong $\left(0.0768\right)=1.193$

from (1) $1500=R\left[\frac{1.193-1}{0.015}\right]$

$1500=R\times \frac{0.193}{0.015}$

$1500=R\times \frac{193\times 1000}{15\times 1000}$

$R=\frac{1500\times 15}{193}=\frac{22500}{193}=116.58$

$\therefore$ so, the required equal quarterly deposits are $116.58$