MAT-144 · Mathematical Reasoning Topic 04 · Loans
Topic 04 · Review · Q3

Finding the down payment, loan amount, and monthly payment for a loan

Three-part: down payment from the percent of sticker, loan amount from sticker minus down, monthly payment from the L2 amortization formula on the loan amount.

01 Worked Example Video

Every step of Finding the down payment, loan amount, and monthly payment for a loan explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE
02 What This Looks Like on ALEKS

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

Couple buys a starter home

A couple buys a $325,000 starter home with a 12% down payment. Mortgage: 6.5% APR over 30 years.

Find the monthly payment. Type just the number, rounded to the nearest cent.

M = $
Couple buys a vacation cabin

A couple buys a $190,000 vacation cabin with a 15% down payment. Mortgage: 7.25% APR over 30 years.

Find the monthly payment. Type just the number, rounded to the nearest cent.

M = $
First-time homebuyer

A first-time buyer purchases a $245,000 townhouse with a 10% down payment. Mortgage: 5.75% APR over 30 years.

Find the monthly payment. Type just the number, rounded to the nearest cent.

M = $
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.
03 The Rule
down = sticker × down % then loan = sticker − down
M = P(r/12) / (1 − (1 + r/12)−12t) P is the loan, not the sticker
Three parts in a chain: down payment (percent of sticker), loan amount (sticker minus down), monthly payment (amortization formula on the loan). Parts (a) and (b) are arithmetic; only part (c) needs the L2 formula. See it live: the $225,000 loan at 5% over 30 years in the Amortization Sandbox →
Common slips
(1) Used the sticker price as P. P is the amount you finance, not the sticker. Overstates the monthly. (2) Used the down payment as P. P = sticker − down, not the down itself. (3) Used the down percent as the interest rate. The down percent and the APR are two completely different numbers.
04 Practice — Step by Step
Practice this problem step by step
A $250,000 home with 10% down. Mortgage: 5% APR over 30 years. Find the down payment, loan amount, and monthly payment.
Step 1

Compute the down payment

10% of $250,000. Type just the number.
down = $
Step 2

Compute the loan amount

Sticker − down: $250,000 − $25,000.
P = $
Step 3

Compute the monthly payment

With P = 225,000, r/12 = 0.004167, n = 360, compute the monthly. Round to the nearest cent.
M = $
Q2 Q4
MAT-144 · TOPIC 04 · REVIEW · Q3 OF 06