at what rate of interest compunded

quaterly for 2.5 years will RS2500 amount
to RS 3900

To find the rate of interest compounded quarterly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = amount after interest
P = principal amount (initial amount)
r = rate of interest (as a decimal)
n = number of times interest is compounded per year
t = number of years

In this case, the principal amount (P) is RS2500 and the amount after interest (A) is RS3900. The time period (t) is 2.5 years, and the interest is compounded quarterly, which means n = 4.

We can rearrange the formula to solve for the rate of interest (r):

r = ( (A/P)^(1/(n*t)) ) - 1

Substituting the given values:

r = ( (3900/2500)^(1/(4*2.5)) ) - 1

Calculating this gives us:

r ≈ 0.0563

Therefore, the rate of interest compounded quarterly for 2.5 years at which RS2500 will amount to RS3900 is approximately 5.63%.