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 Mini-Lesson Video

▸ VIDEO COMING SOON

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

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 v1

A couple plans to purchase a starter home. The bank requires a 12% down payment on the $325,000 home. The couple will finance the rest of the cost with a fixed-rate mortgage at 6.5% annual interest with monthly payments over 30 years.

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

Couple buys a vacation cabin v2

A couple buys a vacation cabin priced at $190,000. The bank requires a 15% down payment. They finance the rest at 7.25% APR over 30 years.

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

First-time homebuyer v3

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

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

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 How to Solve It

Sticker price → split → amount financed → monthly payment. The down payment is multiplication; the loan amount is subtraction; only the monthly payment needs the L2 formula.

down = sticker × down %
loan amount = sticker − down
M = P(r/12) / (1 − (1 + r/12)^−12t)

Parts (a) and (b) are arithmetic; only part (c) needs the amortization formula. Always solve in order.

Compute the down payment (part a).

12% of $325,000.

down = 0.12 \times 325,000 = $39,000

Compute the loan amount (part b).

Sticker minus down. (Equivalently, 88% of sticker.)

P = 325,000 - 39,000 = $286,000

Compute the monthly payment (part c).

P = $286,000, r = 0.065, t = 30. r/12 ≈ 0.005417, n = 360.

M = (286,000 \times 0.005417) / (1 - 1.005417 -360) \approx $1,807.71

Total they'll pay over 30 years: ~$650,777, of which ~$364,777 is interest — more than the loan itself.

▸ COMMON SLIPS(1) Used the sticker price as P. P is what you finance, not what you pay. (2) Used the down payment as P. P = sticker − down. (3) Used the down percent as r. Different numbers; the down percent and the interest rate are unrelated.

04 Practice — Step by Step

Try the vacation cabin scenario. Same three steps.

Compute the down payment.

A couple buys a $190,000 cabin with a 15% down payment. What's the down payment?

down = $

Compute the loan amount.

From step 1: sticker $190,000, down $28,500. What's the loan amount?

P = $

Compute the monthly payment.

P = $161,500, r = 7.25% APR, t = 30 years. Find the monthly payment.

M = $

▸ NICE WORK

You've walked through the whole problem.

That's the move. ALEKS will give you a different version with different numbers — but the steps are the same.

Q2 Q4