It must be invested at 4.5%.
The compound interest formula is
A=p(1+(r/n))^(nt), where A is the total amount including interest earned, p is the principal invested, r is the rate, n is the number of times per year the interest is compounded, and t is the number of years.
With our information we have:
6500=5200(1+(r/4))^(4×5)
6500=5200(1+(r/4))^20
Cancel 5200 by dividing:
6500/5200 = [5200(1+(r/4))^20]/5200
1.25=(1+(r/4))^20
Using a calculator, take the 20th root of each side:
1.25^(1/20) = [(1+(r/4))^20]^(1/20)
1.011219651 = 1+(r/4)
Subtract 1 from each side:
1.011219651-1 = 1+(r/4)-1
0.011219651=r/4
Multiply each side by 4:
0.011219651×4 = (r/4)×4
0.0448786 = r
0.045 = r
