Question

PLEASE HELP!! A Chevrolet Sonic Hatchback costs $14,820.00. With a 15%​ down payment, you can have an amortized loan for 6 years at a rate of 5%​.

a) What will the monthly payment be?

b) How much will the car cost, in total?

c) How much money will be paid in interest?

Answer 1

Using simple interest, it is found that:

a) The monthly payment will be of $227.45.

b) In total, the car will cost $18,599.1.

c) $16,376.1 will be paid in interest.

The amount of money after t years in simple interest is modeled by:

$A(t) = A(0)(1 + rt)$

In which:

• A(0) is the initial amount.
• r is the interest rate, as a decimal.

Item a:

The down payment is 15% of the cost of $14,820.00, hence:

$D = 0.15(14820) = 2223$

The remaining amount accrues interest, hence:

• The initial amount is $A(0) = 14820 - 2223 = 12597$
• Rate of 5%, hence $r = 0.05$
• Paid over 6 years, hence $t = 6$

The total amount that will be paid from the loan is:

$A(t) = A(0)(1 + rt)$

$A(6) = 12597(1 + (0.05)6)$

$A(6) = 16376.1$

Over 6 x 12 = 72 months, hence:

12376.1/72 = $227.45.

The monthly payment will be of $227.45.

Item b:

The payments are divided by:

• Down payment of $2,223.
• Interest of $16,376.1.

Hence:

$T = 2223 + 16376.1 = 18599.1$

In total, the car will cost $18,599.1.

Item c:

From item a, $16,376.1 will be paid in interest.

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