Question

if the simple interest on a sum at 4 per annum for 2 years is rupees 80 then the compound interest on the same sum for the period is​

Answer 1

Answer:

Rs 81.6

Step-by-step explanation:

Given :

Simple interest = Rs 80

Rate = 4 %

Time = 2 years.

We have formula for SI

SI = P R T / 100

P = CI × 100 / R T

P = 80 × 100 / 8

P = Rs 1000

Now for compound interest :

CI = A - P

We have formula for A :

$\displaystyle{\text{A}=\text{P}\left(1+\dfrac{\text{R}}{100}\right)^n }$

Putting values here :

$\displaystyle{\text{A}=1000\left(1+\dfrac{4}{100}\right)^2 }$

$\displaystyle{\text{A}=1000\left(1+0.04\right)^2}\\\\\displaystyle{\text{A}=1000\left(1.04\right)^2}\\\\\displaystyle{\text{A}=1000\times1.04\times1.04}\\\\\displaystyle{\text{A}=1,081.6}$

Now , for CI

CI = 1,081.6 - 1,000

CI = Rs 81.6

Hence we get answer.

Answer 2

$\bold{\underline{\underline{Answer:}}}$

Compound interest = ₹ 81.6

$\bold{\underline{\underline{Step\:-\:\:by\:-\:step\:explanation:}}}$

Given :

• Simple interest (SI) = ₹ 80
• Rate of interest (r) = 4%
• Time period (n) = 2 years

To find :

• Compound interest on the same sum.

Solution :

First we will calculate the principal amount.

For this, since we have the simple interest, time period and rate interest, we can use the formula for simple interest and calculate the principal.

$\bold{\underline{\underline{Formula:}}}$

$\rightarrow$ $\bold{\sf{SI={\dfrac{P\times\:r\times\:n}{100}}}}$

Block in the values,

$\rightarrow$ $\bold{80={\frac{P\times\:4\times\:2}{100}}}$

$\rightarrow$ $\bold{80={\frac{P\times\:8}{100}}}$

$\rightarrow$ $\bold{P\times\:8=100\times\:80}$

$\rightarrow$ $\bold{P={\dfrac{8000}{8}}}$

$\rightarrow$ $\bold{P\:=\:1000}$

•°• Principal Amount (P) = ₹ 1000

Now to CA the compound interest.

$\bold{A=P\:=\:(1 + {\dfrac{r}{100})^n}}$

Block in the values,

$\rightarrow$$\bold{A=1000\:(1 + {\dfrac{4}{100})^2}}$

$\rightarrow$$\bold{A=1000\:\times\:1 + 00.4^2}$

$\rightarrow$$\bold{A=1000\times\:1.04^2}$

$\rightarrow$$\bold{A=\:1000\times\:1.04\times\:1.04}$

$\rightarrow$$\bold{A=\:1,040\times\:1.04}$

$\rightarrow$$\bold{A=\:1,081.6}$

•°• Amount = ₹ 1,081.6

Now, we know that Compound Interest can be calculated by amount from principal.

•°• CI = Amount - Principal

Block in the values,

$\rightarrow$ $\bold{CI=\:1081.6-1000}$

$\rightarrow$ $\bold{CI=81.6}$

•°• Compound interest = ₹ 81.6