Name: Introduction to Compound Interest
Uploaded: 2019-07-19
Duration: 14 min 11 s
Description: In this video, we will discuss the basic concepts and applications of the topic compound interest. This video will be helpful for various competitive examina...

Question

A sum of money amounts to $₹ 13, 230$ in one year and $₹ 13, 891.50$ in $1 \frac{1}{2}$ years at compound interest compounded semi-annually. Find the sum and the rate of interest per annum.

Accepted Answer

Given: A sum of money amounts to $(A) = ₹ 13, 230$ annually

Time $(n) = 1$ year

A sum of money amounts to $(A) = ₹ 13, 891.50$ semi annually

Time $(n) = 1 \frac{1}{2}$ years

Difference between the amounts $= ₹ 13891.50 - ₹ 13230 = ₹ 661.50$

Here $₹ 661.50$ is the interest on $₹ 13230$ for $1 \frac{1}{2}$ years
We know that, $S I = \frac{P T R}{100}$

$\Rightarrow R = \frac{S I \times 100}{P T}$

$\Rightarrow R = \frac{661.50 \times 100 \times 2}{13230 \times 1}$

$\Rightarrow R = 10 %$
We have, amount compounded semi-annually, $A = P {(1 + \frac{R}{200})}^{n}$

$\Rightarrow 13891.50 = P {(1 + \frac{10}{200})}^{3}$

$\Rightarrow 13891.50 = P {(1 + \frac{1}{20})}^{3}$

$\Rightarrow 13891.50 = P {(\frac{21}{20})}^{3}$

$\Rightarrow 13891.50 \times \frac{20}{21} \times \frac{20}{21} \times \frac{20}{21} = P$

$\Rightarrow P = ₹ 12000$

Therefore, rate of interest is $10 %$ and principal amount is $₹ 12000$

S Purkayastha Solutions for Chapter: Compound Interest, Exercise 7: BRAIN WORKOUT

S Purkayastha Mathematics Solutions for Exercise - S Purkayastha Solutions for Chapter: Compound Interest, Exercise 7: BRAIN WORKOUT

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