Question

a sum of money invested at compound interest becomes rupees 1020 after 3 years and rupees 1088 after 4 years find the rate of interest

Answer 1

3rd years amount is sum for 4th year


p(1+r/100)^t=amount

1020(1+r/100)^1= 1088

(1+r/100) =1088/1020

r/100=68/1020

r=6800/1020
r= 6.67 %
so Rate is 6.67%

Answer 2

Answer:

The Principal is Rs. 840.

Step-by-step explanation:

Given:

Amount after 3 years = 1020

Amount after 4 years = 1088

Let the principal be P

and the rate of interest be R

We know that A = P (1 + $\frac{R}{100}$ )ⁿ

where A is the amount

           P is the principal

          R is the rate

          n is the no. of years

Therefore, on substituting the values, we get,

1020 = P (1 + $\frac{R}{100}$ )³           --(i)

1088 = P (1 + $\frac{R}{100}$ )⁴           --(ii)

Dividing equation (i) and (ii),

=> $\frac{1020}{1088}$ = $\frac{1}{1 + \frac{R}{100} }$

=> $\frac{1020}{1088}$ = $\frac{1}{ \frac{100+R}{100} }$

=> $\frac{1020}{1088}$ = $\frac{100}{100+R}$

=> 1020(100+R) = 1088*100

=> 102000 + 1020 R = 108800

=> 1020 R = 108800 - 102000

=> 1020 R = 6800

=> R = 6.67%

Therefore, to find the Principal, substituting the value of R in equation (i)

=> 1020 = P (1 + $\frac{6.67}{100}$ )³  

=> 1020 = P (1.2137)

=> P ≈ 840.405

On rounding off, we get the Principal to be Rs. 840.