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

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

Given that:

• For loan F: Interest rate is 5.66% compounding  monthly.

• For loan G: Interest rate is 6.02% compounded semi-annually.

Calculations:

Effective rate for loan F will be calculated as:

$r = (1 + \dfrac{0.0566}{12})^{12} - 1 \: \: ; n = 12\\or\\r = 0.0580916$

Effective rate for loan G:

$r = (1 + \dfrac{0.0602}{2})^{2} - 1 \: \: ; n = 2\\or\\r = 0.061106$

Thus the difference between effective rate of loan G from that of loan F is

$= 0.061106 - 0.058091\\\approx 0.00302\\or\\0.00302 \times 100 \: percent\\\\= 0.302 \: percent$

Thus option C is correct.

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