The annual interest rate will be 5.04% if the compounded quarterly provides this return.
The annual interest rate means the rate paid on investments without accounting for the compounding of interest within that year.
Let assume that PV = $100
Future Value = $100*(1+2.5)
Future Value = $100*3.5
Future Value = $350
Periods = Years*frequency
Periods =25 *4
Periods = 100
Quarterly Rate = (FV/PV)^(1/Periods)-1
Quarterly Rate = (350/100)^(1/100) - 1
Quarterly Rate = 1.01260642915 - 1
Quarterly Rate = 0.01260642915
Annual rate = Quarterly rate * Frequency
Annual rate = 0.01260642915 * 4
Annual rate = 0.0504257166
Annual rate = 5.04
in conclusion, the annual interest rate will be 5.04% if the compounded quarterly provides this return.
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