Finding the present value of an investment earning compound interest

Reverse direction. You know what the account has to be worth at the end; find what to put in now. Same formula as Q4, solved for P.

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.

Elsa's retirement

To help with her retirement savings, Elsa wants $20,000 in 10 years. The account pays 3.6% compounded quarterly.

How much should she invest now? Type just the number.

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

P = $

Dev's tuition fund

Dev needs $7,500 in 8 years for tuition. He finds an account paying 5.2% compounded semiannually.

How much should he deposit today? Type just the number.

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

P = $

Priya's twenty-year plan

Priya wants $45,000 in 20 years. The account pays 2.9% compounded monthly.

How much should she invest now? Type just the number.

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

P = $

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

$A = P\left(1 + \tfrac{r}{n}\right)^{nt}$ the same formula you used in Q4

solve for P → $P = \dfrac{A}{\left(1 + \tfrac{r}{n}\right)^{nt}}$ build the growth factor, then divide instead of multiply

Nothing new to memorise. Build $\left(1 + \tfrac{r}{n}\right)^{nt}$ exactly as before, then divide the target amount by it instead of multiplying the principal by it. The growth factor is always bigger than 1, so your answer must come out smaller than the target. That is the sanity check.

Common slips

(1) Multiplied instead of divided. If your answer is larger than the target, you ran it forwards. (2) Subtracted the interest. $A - I$ is not the present value; compound growth is not linear. (3) Rounded the growth factor. Over 64 quarters a fourth-decimal truncation moves the answer by dollars, not cents. Carry it all.

04 Practice — Step by Step

Work it in three moves

Marcus wants $9,000 in an account 5 years from now. The account pays 4.8% compounded monthly.

How much does he need to invest today?

Step 1

Find the periodic rate

Divide the annual rate by the number of periods per year: 0.048 ÷ 12.

r/n =

Step 2

Count the periods

How many compounding periods in 5 years at 12 per year?

nt =

Step 3

Divide by the growth factor

$(1.004)^{60} = 1.2706407187$. Now divide $9,000 by that. Round to the nearest cent.

P = $

Q4 Q6

Finding the present value of an investment earning compound interest

The whole move