Question 25 • 26-27 Ignite Technical Math-Financial Math - MA2007
Say you are considering two loans. Loan F has a nominal interest rate of 5.66%, compounded monthly. Loan G has a rate of 6.02%, compounded semiannually. Which loan will give the lower effective interest rate, and how much lower will it be?
Answer
A
Loan G’s effective rate will be 0.091 percentage points lower than Loan F’s.
B
Loan G’s effective rate will be 0.058 percentage points lower than Loan F’s.
C
Loan F’s effective rate will be 0.302 percentage points lower than Loan G’s.
D
Loan F’s effective rate will be 0.149 percentage points lower than Loan G’s.
Explanation
For a nominal rate compounded monthly, Loan F’s effective rate is (1 + 0.0566/12)^12 − 1 ≈ 5.809%. For Loan G, compounded semiannually, it is (1 + 0.0602/2)^2 − 1 ≈ 6.111%. Loan F’s effective rate is lower by about 6.111% − 5.809% = 0.302 percentage points, so the correct choice is “Loan F’s effective rate will be 0.302 percentage points lower than Loan G’s.”
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