Question

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?

Answer 1

The monthly payments on a $12,000 car loan at 3% compounded monthly for 4 years would be approximately $268.37. The total interest paid over the life of the loan would be approximately $2,208.44.

Step-by-step explanation:

To calculate the monthly payments on a car loan, we can use the formula for the present value of an annuity:

Monthly Payment = P * (r(1+r)n) / ((1+r)n - 1)

where P is the principal amount, r is the monthly interest rate, and n is the number of months. For this specific case, the principal amount is $12,000, the monthly interest rate is 3% divided by 100 and divided by 12, and the number of months is 4 years multiplied by 12. Plugging these values into the formula, we get:

Monthly Payment = $12,000 * (0.03/12(1+0.03/12)4*12) / ((1+0.03/12)4*12 - 1)

Calculating this expression gives us a monthly payment of approximately $268.37.

To calculate the amount of interest paid over the life of the loan, we can use the formula for the total interest paid on an annuity:

Total Interest = (Monthly Payment * n) - P

where P is the principal amount and n is the number of months. Plugging in the values, we get:

Total Interest = ($268.37 * 4*12) - $12,000

Calculating this expression gives us a total interest payment of approximately $2,208.44.

Answer 2

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