Question

The simple interest on a sum of money
for 2 years at 8% per annum is 2400.
What will be the compound interest on
that sum at the same rate and for the
same period?​

Answer 1

SOLUTION:-

CALCULATION OF SIMPLE INTEREST

GIVEN

°TIME=2YEARS

°RATE=8%

°INTEREST=₹2400

*SO,

PRINCIPAL=SI*100/R*T

=2400*100/8*2

=150*100

=15000

CALCULATION OF COMPOUND INTEREST

HERE

•PRINCIPAL=15000

•TIME=2YEARS

•RATE=8%

*SO,

COMPOUND INTEREST=P[(1+R/100)^n-1]

=15000[1+8/100)²-1]

=15000[(108/100)²-1]

=15000[27/25*27/25-1]

=15000[729/625-1]

=15000[729-625/625]

=15000*104/625

=24*104

=₹2496

Answer 2

Given:-

• The simple interest on a sum of money for 2 years at 8% per annum is 2400.

To find:-

• The compound interest on that sum at the same rate and for the same period?....?

Solutions:-

• Simple interest (SI) = Rs 2400

• Rate of interest, R = 8%

• Time, n = 2year

The principal can be calculated using the formula:

$\leadsto \: \: sum \: \: = \: \: Rs \: \: {(\frac{{100} \: \times \: {SI}}{R \: \times \: T})}$

$\leadsto \: \: sum \: \: = \: \: Rs \: \: {(\frac{{100} \: \times \: {2400}}{{8} \: \times \: {2}})}$

$\leadsto \: \: sum \: \: = \: \: Rs \: \: {50} \: \times \: {300}$

$\leadsto \: \: sum \: \: = \: \: Rs \: \: {15000}$

i.e., the principal is Rs 15000

The amount including the compound interest.

$\leadsto \: \: Amount \: \: = \: \: P \: \: {({1} \: + \: \frac{R}{100})}^{n}$

$\leadsto \: \: Amount \: \: = \: \: Rs \: {15000} \: \: {({1} \: + \: \frac{8}{100})}^{2}$

$\leadsto \: \: Amount \: \: = \: \: Rs \: {15000} \: \: {(\frac{{100} \: + \: {8}}{100})}^{2}$

$\leadsto \: \: Amount \: \: = \: \: Rs \: {15000} \: \: {(\frac{108}{100})}^{2}$

$\leadsto \: \: Amount \: \: = \: \: Rs \: {15000} \: \times \: {1.08} \: \times \: {1.08}$

$\leadsto \: \: Amount \: \: = \: \: Rs \: \: {17496}$

i.e., the amount including the compound interest is Rs. 17496

Compound interest = Rs (17496 - 15000)

= Rs. 2496

Hence, The compound interest on that sum at the same rate and for the same period is Rs. 2496.