Q:

Ross Land has a loan of​ $8,500 compounded quarterly for four years at 4 ​%.What is the effective interest rate for the​ loan?

Accepted Solution

A:
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 4yrPeriod 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 = 16The 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 yearNow APR can be calculated asAPR = 366.75/8500 = 0.0430 = 4.30%Hence, the effective interest rate for the​ loan is 4.30%.