Question

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? 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.

Answer 1

When the effects and impacts of compounding over time are taken into account, the effective annual interest rate is the true return on a savings account or any other interest-paying investment.

Option C is the correct answer:  Loan F's effective rate will be 0.302 percentage points lower than Loan G's.

Given

The interest rate on loan F is 5.66 percent per month, compounded.

The interest rate on loan G is 6.02 percent, compounded semi-annually.

Computations of effective rates

$\text{Effective rate for loan F}:\\\\r = 1+\frac{0.0566}{12}^{12} - 1 \\\\\n=12\\\\\\text{or}\\\\\r=0.0580916\\\\\\\text{Effective rate for loan G}\\\\r = 1+\frac{0.0602}{12}^{2} - 1 \\\\\\n = 2\\\text{or}\\\\\r=0.0611106\\\\\\\text{ The difference between the loans for G and F}:\\\\=0.061106-0.058091\\\\=0.00302\\\\\text{or}\\\\=0.00302 \text{ x } 100\\\\=0.302 \text{percent}$

Therefore, option c is the correct answer.

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