Question

The compound interest on a certain some of money at 5% per annum
for two years is 246. Calculate the S.I on the same sum for three
years at 6% per annum.​

Answer 1

Answer:

SI=432

Step-by-step explanation:

CI=246, R=5%, T=2 years

Let the principal be x

A=P(1+R/100)^T

A=x(1+5/100)^2

A=x×21/20×21/20=441/400x

We have CI=A-P

246=441/400x-x

246=441-400/400

246=41/400

x=246×400/41= 2400 rupees

Now, given rate=6%

Time=3years

SI=P×R×T/100

SI=2400×6×3/100

SI=432 rupees

I hope this answer will help you

Answer 2

Given :

• Compound Interest (CI) = Rs.246
• Rate of Compound interest (R) = 5%
• Time period = 2 years

To Find :

• Simple Interest as per conditions

Conditions :

• Rate of Simple Interest (R) = 6%
• Time period of simple Interest = 3 years

Formulas Applied :

• It's given that the compound interest of certain amount for 2 years at 5% is Rs.246. So we have to find the certain amount which can be termed as principle amount to find the simple Interest as per given conditions. It's given the compound interest of principle amount. So let's find the principle by substituting the values in formula of Compound Interest as shown as below :

$\underline{\boxed{\sf Compound \: Interest= P\bigg[\Big(1+\dfrac{R}{100}\Big)^t - 1\bigg]}}$

• We have to find simple Interest on certain amount. So let's substitute values in formula of simple Interest to fine simple Interest as shown as below :

$\underline{\boxed{\sf Simple\: Interest = \bigg(\dfrac{PRT}{100}\bigg)}}$

Solution :

${\longrightarrow \sf CI = P\bigg[\Big(1+\dfrac{R}{100}\Big)^t - 1\bigg]}\\\\{\longrightarrow \sf 246 = P\bigg[\Big(1+\dfrac{5}{100}\Big)^2- 1\bigg]}\\\\{\longrightarrow\sf 246 = P \bigg[\Big(\dfrac{100+5}{100}\Big)^2-1\bigg]}\\\\{\longrightarrow \sf 246 = P \bigg[\Big(\dfrac{105}{100}\Big)^2-1\bigg]}\\\\{\longrightarrow \sf 246 P \bigg[\Big(\dfrac{11025}{10000}\Big)-1\bigg]}\\\\{\longrightarrow \sf 246 = P \bigg[\dfrac{11025-10000}{10000}\bigg]}\\\\{\longrightarrow \sf 246 = P \bigg[\dfrac{{\cancel{1025}}^{41}}{{\cancel{10000}}^{400}}\bigg]}\\\\{\longrightarrow \sf P= \bigg[\dfrac{{\cancel{246 }}^6\times 400}{{\cancel{41}}_1}\bigg]}\\\\{\longrightarrow\sf 2400}$

Simple Interest :

${\longrightarrow \sf Simple \: Interest=\dfrac{24{\cancel{0}}{\cancel{0}}\times 6 \times 3}{1{\cancel{0}}{\cancel{0}}}}\\\\ {\longrightarrow \sf 24 \times 6 \times 3}\\\\{\longrightarrow \sf 24 \times 18}\\\\{\longrightarrow \sf 432 }$

Required Answer :

Simple Interest as per given conditions is $\underline{\sf Rs.432}$