Question

1a. If you take out a car loan for $30,000 for 6 years at 4.5% Simple interest what is the monthly payment? and How much will you pay in total for interest at the end of the 6 years?

1b. If you take out a car loan for $30,000 for 6 years at 4.5% Compound Interest what is the monthly payment? and How much will you pay in total for interest at the end of the 6 years?

Answer 1

1a.

Interest is determined at simple interest rate and add on the amount of the loan

Amount of loan and interest is the future value of the loan

FV=P(1+rt)

P =amount of the car loan=$30,000

r=4.5% or 0.045

t=6yrs

FV=30,000(1+0.045×6)=30,000×1.27=38,100

Now we know how much to pay in total for the Car.

We still have to find out how much this will cost in monthly payment

So,divide the FV by number of months(6×12=72)

Monthly payment =$38,100/72= $529.17

monthly payment for car loan would be $529.17

Interest amount = FV - Car Loan amount

=$38,100-$30,000=$8,100

Total Interest at the end of 6year is $8,100

1b.

Compound interest monthly payment

PV= R'[1-(1+i)^-n]÷i

PV =present loan amount=$30,000

R=regular payments

i= interest rate 4.5% compounded monthly= (0.045/12)

n = time period =6yrs×12=72times

$30,000=R[1-(1+0.045/12)^-6×12]/(0.045/12)

R=$30,000×(0.045/12) ÷ [1-(1+0.00375)^-72]

R=$30,000(0.045/12)÷ [1-(1.00375)^-72]

R=112.5÷ (1-0.7637)= 112.5÷0.236=$476.69

Monthly payment =$476.69

Car monthly payment would be $476.69

Interest = monthly payment ×no.of months - car loan

Interest = $476.69×72-$30,000

Interest = $ 34,322.033 - $30,000= $4,322.033

The total Interest at the end of the 6years would be $4,322