You decide finance a $12,000 car at 3% compounded monthly for 4 years. What will your monthly payments be? How much interest will you pay over the life of the loan?

Step-by-step explanation:

The cost of the car is $12,000

We would apply the periodic interest rate formula which is expressed as

P = a/[{(1+r)^n]-1}/{r(1+r)^n}]

Where

P represents the monthly payments.

a represents the cost of the car

r represents the interest rate

n represents number of monthly payments. Therefore

a = 12000

r = 3%/12 = 0.03/12 = 0.0025

n = 12 × 4 = 48

Therefore,

P = 12000/[{(1+0.0025)^48]-1}/{0.0025(1+0.0025)^48}]

12000/[{(1.0025)^48]-1}/{0.0025(1.0025)^48}]

P = 12000/{1.127 -1}/[0.0025(1.127)]

P = 12000/(0.127/0.0028175)

P = 12000/45.075

P = $266.22

The monthly payment is $266.22

The total amount that would be paid over the life of the loan is

266.22 × 48 = $12778.56

The amount of interest paid is

12778.56 - 12000 = $778.56