Question

On a certain sum of money, the difference between the CI for a year, payable half-yearly and the SI for a year is

₹ 120

. Find the sum lent out, if the rate of interest in both cases is

10 %

per annum.

Accepted Answer

Given, on a certain sum of money, the difference between the CI for a year, payable half-yearly and the SI for a year is $₹ 120$ .

Rate of interest in both cases is $10 %$ per annum.

Let the given sum be $₹ P$ .

Simple interest $= \frac{P R T}{100}$ , where $P$ is the principal, $R$ is the rate of interest and $T$ is the time period

$∴ \frac{P \times 10 \times 1}{100} = \frac{P}{10}$

When the interest is compounded half-yearly, we use the formula, compound interest $= P {(1 + \frac{R}{200})}^{2 T} - P$ , where $P$ is the principal, $R$ is the rate of interest and $T$ is the time period.

$∴$ Compound interest $= P {(1 + \frac{10}{200})}^{2} - P$

$= P {(1 + \frac{1}{20})}^{2} - P$

$= P {(\frac{21}{20})}^{2} - P$

$= \frac{441 P}{400} - P$

$= \frac{441 P - 400 P}{400}$

$= \frac{41 P}{400}$

$∴$ Compound interest $-$ Simple interest $= 120$

$\Rightarrow \frac{41 P}{400} - \frac{P}{10} = 120$

$\Rightarrow \frac{41 P - 40 P}{400} = 120$

$\Rightarrow P = 120 \times 400$

$\Rightarrow P = 48000$

Hence, the required sum is $₹ 48000$ .

B Nirmala Shastry Solutions for Exercise 1: EXERCISE 2A

B Nirmala Shastry Mathematics Solutions for Exercise - B Nirmala Shastry Solutions for Exercise 1: EXERCISE 2A

Questions from B Nirmala Shastry Solutions for Exercise 1: EXERCISE 2A with Hints & Solutions

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