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MAT-144 · In-person sections Exam 2 Review · Unit 2
Exam 2 Review · Q7

Finding the periodic payment needed to meet an investment goal

You know the target and the deadline; find the deposit. The annuity formula from Q6, solved for PMT.

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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.

Leila's motorcycle

Leila invests in an ordinary annuity earning 4.8% compounded monthly, paying in at the end of each month.

How much must she pay in each month for the annuity to be worth $10,000 after 4 years? Type just the number.

Do not round intermediate computations; round the final answer to the nearest cent.

PMT = $
The Byrne family's quarterly plan

The Byrnes pay into an ordinary annuity at the end of every quarter. It earns 5.5% compounded quarterly.

What quarterly payment reaches $50,000 in 10 years? Type just the number.

Do not round intermediate computations; round the final answer to the nearest cent.

PMT = $
Reading the trap

A student needs $6,000 in 3 years and will pay monthly into an annuity at 7.2% compounded monthly.

Find the monthly payment. Type just the number.

Do not round intermediate computations; round the final answer to the nearest cent.

PMT = $
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.
\(FV = PMT \times \dfrac{(1 + i)^{N} - 1}{i}\) the Q6 formula, with i the periodic rate and N the number of payments
solve for PMT → \(PMT = \dfrac{FV \times i}{(1 + i)^{N} - 1}\) the same bracket, now on the bottom
Build \((1 + i)^{N} - 1\) exactly as you would for Q6. The only change is where it sits: multiply by it to find a total, divide by it to find a payment. Note the − 1 is inside the bracket and gets subtracted before you divide.
Common slips
(1) Divided the goal by the number of payments. $6,000 over 36 months is not $166.67 — interest does part of the work, so the payment is smaller. (2) Forgot the − 1. Subtract it before dividing, not after. (3) Used the annual rate as i. Monthly payments need the monthly rate and the monthly count: i = r/12 and N = 12t.
Three moves again

Rosa wants $25,000 in 5 years for a deposit on a house. Her account pays 6% compounded monthly and she will deposit the same amount at the end of every month.

How much must she deposit each month?

Step 1

Periodic rate and payment count

What is the monthly rate i?
i =
Step 2

Build the bracket

\((1.005)^{60} = 1.3488501525\). Subtract 1, then divide by i = 0.005. Round to four decimals.
Step 3

Divide the goal by the factor

25,000 ÷ 69.7700. Round to the nearest cent.
PMT = $
Q6 Q8