Question

You are going to buy a new car worth $23,800. The dealer computes your monthly payment to be $510.45 for 60 months of financing. What is the dealer's effective rate of return on this loan transaction? The dealer's effective rate of return is %. (Round to one decimal place.)

Answer 1

Price of the car=PV=$23800

Monthly installment=R=$510.45

Period=n=60 months

Let the monthly interest rate be i. So

PV=R*(P/A,i,60)

23800=510.45*(P/A,i,60)

(P/A,i,60)=(23800/510.45)=46.6255

I shall use try and error method to estimate the i

Let us first try at i=1%

(1+i)" (P/A, i,n)=-

1- (P/A, 0.01,60) = - (1+0.0160 - = 44.9550 0.01

Our interest factor is higher than (P/A,0.01,60). So, let us try at lower interest rate say 0.9% and 0.85%

1- 10.00960 (P/A, 0.009, 60) = 2 - = 46.2047 0.009

1-140, 0085) (Ρ/Α, 0.0085, 60) =- - = 46.8481 0,0085

Out interest factor (P/A,i,60) lies between above two interest factors, We can say that i is between 8.5% and 9%

Let is try at 8.6%, and 8.7%

1 - (1+0.0086 60 (P/A, 0.0086,60) = – -= 46.7184 0.0086

1-140.0087) (Ρ/Α, 0.0087, 60) =- 46.5892 0.0087

Let us try at i=8.65%, 8.66% and 8.67%

1- (1+0.00865)60 = 46.6538 (P/A, 0.00865,60) = – 0.00865

1- (1+0.0086660 (P/A, 0.00866,60) = - - = 46.6408 0.00866

1- (1+0.00867)60 (P/A, 0.00867, 60) = – - = 46.6279 0.00867

We can see our (P/A,i,60) value is quite close to value of (P/A,0.00867,60)

We can say that i=0.867%

(We can also get this value by using Excel or financial calculators. Exact value is 0.8672%)

Effective return=(1+0.00867)^12-1=10.91% or say 10.9%