Kriti invested a given amount in a scheme and at the end of 3 years it was worth Rs. 4,960. At the endof another 5 years, it was worth Rs. 5,600. What is the rate of interest earned, if interest is earned onlyon the principal?
Answers
The rate of interest is 8 % per annum.
Kriti invested a given amount in a scheme and at the end of 3 years it was worth Rs. 4,960. At the end of another 5 years, it was worth Rs. 5,600.
We have to find the rate of interest earned, if interest is earned only on the principal.
“It was mentioned that the interest is earned only on the principal”, which means, interest applying on it is simple interest.
Let the rate of interest is r % per annum and P is principal.
case 1 : A = 4,960 , t = 3 years
⇒SI = (P × r × t)/100
= (P × r × 3)/100
= 3Pr/100
so, A = P + SI = P + 3Pr/100
⇒4960 = P(100 + 3r)/100 ...(1)
case 2 : A = 5600, t = 5 years
SI = (P × r × t)/100
= (P × r × 5)/100
= 5Pr/100
so, A = P + SI = P + 5Pr/100
⇒5600 = P(100 + 5r)/100 ...(2)
from equations (1) and (2) we get,
⇒4960/5600 = (100 + 3r)/(100 + 5r)
⇒31/35 = (100 + 3r)/(100 + 5r)
⇒3100 + 155r = 3500 + 105r
⇒50r = 400
⇒r = 8 %