Final answer:
To find the interest rate compounded quarterly that is equivalent to an effective interest rate of 5.07%, you can use the formula for compound interest.
Step-by-step explanation:
To find the interest rate compounded quarterly that is equivalent to an effective interest rate of 5.07%, you can use the formula for compound interest:
Effective interest rate = (1 + (interest rate / number of compounding periods))^number of compounding periods - 1
Let's plug in the values:
5.07% = (1 + (interest rate / 4))^4 - 1
Now, solve the equation for the interest rate by isolating it:
(1 + (interest rate / 4))^4 = 1.0507
Take the fourth root of both sides:
1 + (interest rate / 4) = 1.0149
Subtract 1 from both sides:
interest rate / 4 = 0.0149
Multiply both sides by 4:
interest rate = 0.0596
Therefore, an interest rate of 5.96% compounded quarterly is equivalent to an effective interest rate of 5.07%.