Monthly payment, total payment and interest for a loan

One formula produces the payment. The other two answers are a multiplication and a subtraction hanging off it.

01 Worked Example 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.

The payment

An amortized loan of $30,000 at 5.9% with monthly payments over 6 years.

Find the monthly payment. Type just the number.

The interest

Same loan: $30,000, 72 payments of $495.77.

How much interest is paid in total? Type just the number.

Shorter term

$9,500 at 8.25%, monthly payments 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.

03 The Rule

PMT = P × i ÷ [1 − (1 + i)^−N] the amortization formula

total = PMT × N · interest = total − P parts (b) and (c), one line each

P is the amount borrowed, i is the annual rate divided by 12, and N is the number of monthly payments. The exponent is negative — that minus sign is the single most common source of a wrong answer here.

Common slips

(1) Dropping the minus in the exponent. Produces a plausible-looking payment that is badly wrong. (2) Using N = years. Monthly payments over 8 years is 96, not 8. (3) Subtracting the wrong thing for the interest. Interest is the total minus what was borrowed.

04 Practice — Step by Step

One formula, three answers

Priya took out a personal, amortized loan for $18,000 at an interest rate of 7.2%, with monthly payments for a term of 5 years.

(a) Find her monthly payment.
(b) Find the total amount to repay the loan.
(c) Find the total interest she will pay.

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

Step 1

The periodic rate

7.2% a year, paid monthly. What is i? Give four decimal places.

Step 2

How many payments?

Monthly, for 5 years.

Step 3

Which exponent?

In the denominator, 1 − (1 + i) raised to what?

Step 4

(a) The monthly payment

18,000 × 0.006 ÷ [1 − (1.006)⁻⁶⁰]

Step 5

(b) Total repaid

60 payments of $358.12.

Step 6

(c) Total interest

Subtract what she borrowed.

Q9 Q11

Monthly payment, total payment and interest for a loan

Part (a) is the work, (b) and (c) are free