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MAT-144 · In-person sections Exam 2 Review · Unit 2
Exam 2 Review · Q13

Down payment, loan amount and monthly payment for a loan

Three parts that feed each other. The one that matters is financing the loan, not the sticker price.

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A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

The loan amount

A $38,000 vehicle with a 25% down payment required.

How much is financed? Type just the number.

$
The payment

Same vehicle: $28,500 financed at 6.99% with monthly payments over 6 years.

Find the monthly payment. Type just the number.

$
Small down payment

A $16,400 car with 10% down, financed at 8.99% over 4 years.

Find the monthly payment. Type just the number.

$
Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.
down payment = price × percent part (a)
loan = price − down payment part (b) — and the P for part (c)
PMT = loan × i ÷ [1 − (1 + i)−N] part (c)
Part (b) looks like busywork. It is not: it is there so the loan amount is written down as its own number before you reach for the payment formula. Put the price into that formula and every answer after it is wrong.
Common slips
(1) Financing the full price. The most common error here, and it produces a clean-looking number with no warning attached. (2) Rounding the periodic rate. 9.5% ÷ 12 repeats; keep it in the calculator. (3) N = years. Six years of monthly payments is 72.
Down payment, loan, then payment

Marcus plans to purchase a used van. The dealer requires a 15% down payment on the $24,500 vehicle. Marcus will finance the rest with a fixed-rate amortized auto loan at 8.25% annual interest with monthly payments over 5 years.

(a) Find the required down payment.
(b) Find the amount of the auto loan.
(c) Find the monthly payment.

Do not round intermediate computations. Round final answers to the nearest cent.

Step 1

(a) The down payment

15% of $24,500.
$
Step 2

(b) The loan amount

What is left to finance?
$
Step 3

(c) Which P goes in the formula?

The amortization formula needs the amount borrowed.
Step 4

i and N

How many monthly payments over 5 years?
Step 5

(c) The monthly payment

20,825 × 0.006875 ÷ [1 − (1.006875)−60]
$