Answer:
The effective interest rate for the loan is 4.30%.
Step-by-step explanation:
Consider the provided information.
The loan is $8500 which compounded quarterly for 4 years at 4%.
Annual rate is 0.04 and number of period is 4yr
Period interest rate (R) = [tex]\frac{annual\ rate}{\text{number of period}} = \frac{0.04}{4}= 0.01[/tex]
Compounding periods = n = 4 Comp./yr. × 4yrs = 16
The formula for calculating Future value is:
[tex]FV=PV(1+R)^{nm}[/tex]
Substitute PV = 8500, R = 0.01, n = 16 in above formula,
[tex]FV=8500(1+0.01)^{16}[/tex]
[tex]FV=8500(1.01)^{16}[/tex]
[tex]FV=9967[/tex]
Now calculate interest per year.
[tex]I=\frac{FV-PV}{T}[/tex]
Now substitute the respective values in the above formula..
[tex]I=\frac{9967-8500}{4}[/tex]
[tex]I=\frac{1467}{4}[/tex]
[tex]I=366.75[/tex] interest per year
Now APR can be calculated as
APR = 366.75/8500 = 0.0430 = 4.30%
Hence, the effective interest rate for the loan is 4.30%.
