Jana has $1,500 for a down payment and thinks she can afford monthly payments of $300.If she can finance a vehicle with a 7%,4-year loan,what is the maximum loan amount Jana can afford?
A)$12,528
B)$14,000
C)$16,028
D)$17,900
E)$18,028

Question

Quizplus · Accepted Answer

To calculate the maximum loan amount Jana can afford, we need to use the present value of an annuity formula:
PMT x [(1 - (1+i)^-n)/i] + PV = FV
where PMT is the monthly payment, i is the interest rate per period (in this case, per month), n is the total number of periods (in this case, 48 months), PV is the present value (in this case, the down payment), and FV is the future value (in this case, the maximum loan amount).

Substituting the values given, we have:
$300 x [(1 - (1+0.07/12)^-48)/(0.07/12)] + $1,500 = FV
Simplifying this equation, we get:
FV = $13,622.62

Therefore, the maximum loan amount Jana can afford is $13,622.62. Since the answer choices are rounded to the nearest thousand, the closest choice is B, $14,000.

Jana Has $1,500 for a Down Payment and Thinks She