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:
[tex]A(t) = A(0)(1 + rt)[/tex]
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:
[tex]D = 0.15(14820) = 2223[/tex]
The remaining amount accrues interest, hence:
- The initial amount is [tex]A(0) = 14820 - 2223 = 12597[/tex]
- Rate of 5%, hence [tex]r = 0.05[/tex]
- Paid over 6 years, hence [tex]t = 6[/tex]
The total amount that will be paid from the loan is:
[tex]A(t) = A(0)(1 + rt)[/tex]
[tex]A(6) = 12597(1 + (0.05)6)[/tex]
[tex]A(6) = 16376.1[/tex]
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:
[tex]T = 2223 + 16376.1 = 18599.1[/tex]
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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