Leo is going to the Bank of Montreal for a student loan. He knows that the posted rate is not the true rate as the bank's nominal rate is expressed on an annual basis and does not take into account the effect of compounding over the course of the loan. Leo wants to know what the effective annual interest rate on a $10,000 loan would be if it charges 5% interest, compounded quarterly, and a $300 administration fee up-front?
Question 29Select one:
a.
5.25%
b.
4.92%
c.
4.94%
d.
5.09%
The effective annual interest rate can be calculated using the formula:
EAR = (1 + r/n)^n - 1
Where r is the nominal interest rate and n is the number of compounding periods per year.
In this case, the nominal interest rate is 5% (0.05) and the loan is compounded quarterly, so n = 4.
EAR = (1 + 0.05/4)^4 - 1
EAR = (1 + 0.0125)^4 - 1
EAR = (1.0125)^4 - 1
EAR = 1.05096 - 1
EAR = 0.05096 or 5.096%
So, the effective annual interest rate on the loan would be 5.09%.
Therefore, the correct answer is d. 5.09%