Question

foster financed his honda ridgeline for $46,800 for 72 months at 3.33% apr. he has now paid the truck off and wants to sell it for $21,400. what is the total amount he invested in the car after selling it?
define the variables:
finance amount, (f) = $
apr = %
number of months, (n) =
use the car financing calculator model to type in the variables.
the monthly payment foster has been paying is $ .
total amount paid = monthly payment × number of months
total amount paid to loan = $
foster paid off the car loan. he now has the title in hand and is going to sell the car for $21,400.
total amount paid − price of car sold = total invested
foster invested a total of $ to own the car for three years.

Explanation:

Step1: Identify Variables

Finance amount (\(P\)) = \$46,800, APR = 3.33\%, number of months (\(n\)) = 72. First, convert APR to monthly rate (\(r\)): \(r=\frac{0.0333}{12}\).

Step2: Calculate Monthly Payment

Use the formula for monthly payment of a loan: \(M = P\frac{r(1 + r)^n}{(1 + r)^n - 1}\).
Substitute \(P = 46800\), \(r=\frac{0.0333}{12}\approx0.002775\), \(n = 72\).
\((1 + r)^n=(1 + 0.002775)^{72}\approx1.217\)
Numerator: \(0.002775\times1.217\approx0.003377\)
Denominator: \(1.217 - 1 = 0.217\)
\(M = 46800\times\frac{0.003377}{0.217}\approx46800\times0.01556\approx728.21\)

Step3: Total Amount Paid

Total amount paid = \(M\times n = 728.21\times72\approx52,431.12\)

Step4: Total Invested (Total Paid - Selling Price)

Selling price = \$21,400. Total invested = \(52431.12 - 21400=\$31,031.12\) (approximate, depending on more precise monthly payment calculation).

Answer:

The total amount invested in the car after selling it is approximately \(\$31,031\) (or more precisely calculated as above).