A certain sum is given on compound interest at some rate. the sum amounts to 7350 and 8575 at the end of 2 years and 3 years respectively.the sum given on compound interest is
Answers
Formula:
We know that the formula for Compound interest is C.I = P * ( 1+R/100)^n
(calculating annually)
where, P is Principal or sum given
r is rate of interest
n is no. of years
Given details:
Final amount is Rs.7350 after 2 years.
Final amount is Rs.8575 after 3 years.
Solution:
P(1+R/100)^2 = 7350 … (1)
P(1+R/100)^3 = 8575 …(2)
When equation (2) is divided by equation (1),
(1+R/100) = 8575 / 7350
Substitute above value in equation (1)
P (8575 / 7350)^2 = 7350
P = 7350 * 7350 * 7350 / 8575 * 8575
P = 5400
Therefore, Sum given = Rs.5400
Answer: 5400
1st year’s interest will be the same for both SI and CI.
For the 3rd year,
The interest will be = 8575 – 7350 = 1225
Principal for 3rd year = 7350
Interest for 3rd year = 1225
Let be the principal interest = (1225/7350) × 100 = 50/3%
Interest for 2 years = (50/3)+(50/3)+[(50/3×50/3)/100] = 325/9%
After 2 years,
Amount = 100 + 325/9 = 1225/9
If 1225/9 is the amount, principal = 100
Similarly,
If 7350 is the amount, then the principal will be
= (900/1225) × 7350 = 5400
Hence, Sum = 5400 with the rate of 50/3%