Loan F's effective rate will be 0.302 percentage points lower than Loan G's.
Given that,
Loan F has a nominal interest rate of 5.66%, compounded monthly.
Loan G has a rate of 6.02%, compounded semiannually.
We have to determine,
Which loan will give the lower effective interest rate, and how much lower will it be?
According to the question,
The lower effective rate is determined by the following formula.
[tex]P = \left(1+\dfrac{r}{n}\right)^n - 1[/tex]
Where; r is the interest rate,
And n is the number of compounding periods per year.
Loan F has a nominal interest rate of 5.66%, compounded monthly.
[tex]\rm P = \left(1+\dfrac{0.0566}{12}\right)^{12} - 1\\\\P = \left(1+\0.0047\right)^{12} - 1\\\\P = \left(1.0047\right)^{12} - 1\\\\P = 1.0.581-1\\\\P = 0.0581[/tex]
And Loan G has a rate of 6.02%, compounded semiannually.
[tex]\rm P = \left(1+\dfrac{0.0602}{2}\right)^{2} - 1\\\\P = \left(1+\0.0301\right)^{2} - 1\\\\P = \left(1.0301\right)^{12} - 1\\\\P = 1.0611-1\\\\P = 0.0611[/tex]
The difference between the amount of Loan F and Loan G is,
= 0.0611 - 0.0581 = 0.003
Converting to percentage gives : 0.003 × 100 = 0.3%
Hence, Loan F's effective rate will be 0.302 percentage points lower than Loan G's.
For more details about Interest rates to the link given below.
https://brainly.com/question/12895249
