Question

A person has Rs.$30,000$ to invest.He wants to invest some amount in the fixed deposit and remaining in savings account.The interest rates are $7\%$ and $5\%p.a$ for the fixed deposit and the saving account respectively. Find how he should divide the total amount $Rs.30000$ in two accounts if he wants to get the annual interest as (i) $Rs.1800$ (ii) $Rs.2000$.

Answer 1

Let us assume that the person will invest Rs. $x$ in savings account

Amount invested in the fixed deposit = Rs. $(30,000-x)$

Given the rate of interest in savings and fixed deposits are $5\%$ and $7\%$ p.a. respectively.

Now, total interest got by the person in annum is $\frac{x\times 5}{100}+\frac{(30,000-x)\times 7}{100}$.

i) According to the problem,

$\frac{x\times 5}{100}+\frac{(30,000-x)\times 7}{100}=1800$

$\Rightarrow \frac{x\times 5}{100}+\frac{2,10,000}{100}-\frac{x\times 7}{100}=1800$

$\Rightarrow \frac{x\times 5}{100}-\frac{x\times 7}{100}=1800-2100$

$\Rightarrow \frac{-2x}{100}=-300$

$x=15,000$.

For the first case, he has to invest Rs. $15,000$ in each of the accounts.

ii) For the second case

$\frac{x\times 5}{100}+\frac{(30,000-x)\times 7}{100}=2000$

$\Rightarrow \frac{x\times 5}{100}+\frac{2,10,000}{100}-\frac{x\times 7}{100}=2000$

$\Rightarrow \frac{x\times 5}{100}-\frac{x\times 7}{100}=2000-2100$

$\Rightarrow \frac{-2x}{100}=-100$

$x=5,000$.

In this case, he has to invest Rs. $5,000$ in savings and Rs. $25,000$ in fixed deposit.