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) = ![\frac{annual\ rate}{\text{number of period}} = \frac{0.04}{4}= 0.01](https://tex.z-dn.net/?f=%5Cfrac%7Bannual%5C%20rate%7D%7B%5Ctext%7Bnumber%20of%20period%7D%7D%20%3D%20%5Cfrac%7B0.04%7D%7B4%7D%3D%200.01)
Compounding periods = n = 4 Comp./yr. × 4yrs = 16
The formula for calculating Future value is:
![FV=PV(1+R)^{nm}](https://tex.z-dn.net/?f=FV%3DPV%281%2BR%29%5E%7Bnm%7D)
Substitute PV = 8500, R = 0.01, n = 16 in above formula,
![FV=8500(1+0.01)^{16}](https://tex.z-dn.net/?f=FV%3D8500%281%2B0.01%29%5E%7B16%7D)
![FV=8500(1.01)^{16}](https://tex.z-dn.net/?f=FV%3D8500%281.01%29%5E%7B16%7D)
![FV=9967](https://tex.z-dn.net/?f=FV%3D9967)
Now calculate interest per year.
![I=\frac{FV-PV}{T}](https://tex.z-dn.net/?f=I%3D%5Cfrac%7BFV-PV%7D%7BT%7D)
Now substitute the respective values in the above formula..
![I=\frac{9967-8500}{4}](https://tex.z-dn.net/?f=I%3D%5Cfrac%7B9967-8500%7D%7B4%7D)
![I=\frac{1467}{4}](https://tex.z-dn.net/?f=I%3D%5Cfrac%7B1467%7D%7B4%7D)
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%.