Question

4. Find the rate of compound interest on Rs 4,000 so that it can amount to Rs 4,630.50 in 3 years.​

Answer 1

5%

Step-by-step explanation:

Given:

Principal = Rs 4000

Amount = Rs 4630.50

Time = 3 yr

To find:

Rate of compound Interest

Solution:

let, The rate of interest be x % p.a

Using formula,

$\text{A} = P{(1+\dfrac{r}{100})}^{t} \\ \\ 4630.50 = 4000 {(1 + \frac{x}{100} )}^{3} \\ \\ \frac{4630.5}{4000} = {( 1 + \frac{x}{100}) }^{3} \\ \\ \frac{ \cancel{46305}}{\cancel{40000}} = {( 1 + \frac{x}{100}) }^{3} \\ \\ \frac{9261}{8000} = {( 1 + \frac{x}{100}) }^{3} \\ \\ {( \frac{21}{20}) }^{3} = {( 1 + \frac{x}{100}) }^{3} \\ \\ \frac{21}{20} = 1 + \frac{x}{100} \\ \\ \frac{21}{20} - 1 = \frac{x}{100} \\ \\ \frac{21 - 20}{\cancel{20}} = \frac{x}{\cancel{100}} \\ \\ 1 = \frac{x}{5} \\ \\ x = 5$

Therefore, The required rate of interest is 5% per annum.

${\underline{\text{Formula Of Interests}}}$

$\boxed{\text{S.I}=\dfrac{Prt}{100}}$

Where,

P = Principal

r = rate of interest

t = time

S.I = Simple Interest

Compound Interest Amount

$\boxed{\text{A} = P{(1+\dfrac{r}{100})}^{t}}$