Question 1200899: Dan is contemplating trading in his car for a new one. He can afford a monthly payment of at most $400. If the prevailing interest rate is 3.9%/year compounded monthly for a 48-month loan, what is the most expensive car that Dan can afford, assuming that he will receive $8000 for his trade-in? (Round your answer to the nearest cent.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Answer: $25,750.69
Work Shown:
P = 400 = monthly payment
i = r/12 = 0.039/12 = 0.00325 = decimal form of the monthly interest rate
n = 48 months
L = unknown loan amount
Solve for L
P = (L*i)/( 1 - (1+i)^(-n) )
400 = (L*0.00325)/( 1 - (1+0.00325)^(-48) )
400 = L*0.02253433364068
L = 400/0.02253433364068
L = 17,750.6912952554
L = 17,750.69
Here's a useful calculator to verify the result
https://www.calculatorsoup.com/calculators/financial/how-much-loan-can-i-afford.php
If the trade-in option wasn't available, then the most he can afford would be $17,750.69
Add on the $8000 trade-in value
17750.69 + 8000 = 25,750.69
The most expensive car Dan can afford is $25,750.69
This is assuming all fees are part of that figure.
This means that if the sticker price was say $25,000 and the fees totaled $2000, then that goes over the $25,750.69 threshold.
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