solve the equation for r: 110.25=100(r+1)^5

Question

Assuming that 'r' is the compound interest, given that the future value and present value are given.

I wanted to detrmine the fifth root of (1+r).

Answer 1

FV=110.25, PV=100. The growth is 110.25/100=1.1025=(1+r)^5. Take the fifth root of 1.1025: 1.01971 approx. Use a calculator for this. So 1+r=1.01971 and r=0.01971 or 1.971%. (The exponent 5 represents the number of periods over which compound interest has been applied. It looks like a quarterly rate, so the annual interest rate would be 4*1.971=7.884%.) You needed the fifth root of the growth rather than the fifth root of 1+r, which is raised to the power of 5.