Time Value of Money Practice Problems

Time value of money is one of those concepts that sounds abstract until a student sees it attached to a real number. Explain the formula on a whiteboard and most students nod along and forget it by lunch. Hand them a set of time value of money practice problems built around a specific person, a specific dollar amount, and a specific interest rate, and the concept starts to stick.

That's the approach this activity takes. Every problem centers on a character with a concrete goal: a student saving her first paycheck, a family trying to hit a savings target in four years, a teenager financing a car. Students aren't solving for an abstract "principal" and "rate." They're figuring out how much Diane's $500 grows at 7% interest versus 10%, or what Frank's monthly car payment looks like at 9% interest over 60 months versus 8% over 48. Concrete numbers make the compounding effect visible in a way a formula alone doesn't.

The five problems build in difficulty. The first two work through the same $500 deposit at different interest rates and time horizons, so students can directly compare how a few percentage points compound over 5, 10, and 20 years. The third flips the question around, asking students to solve for the interest rate needed to hit a savings goal instead of solving for the ending balance. The last two apply the same math to a loan instead of a savings account, which is where most students will actually encounter compounding first, in a car payment or a credit card balance.

This activity comes from Rapunzl's Saving vs. Investing unit, where time value of money is introduced as the mechanism that makes both saving and investing pay off over time.

Below are the problems exactly as they appear in the Rapunzl curriculum, followed by notes on how to use them in class.

These time value of money practice problems come from Module 2: Saving vs. Investing in Rapunzl's grades 6–12 curriculum.

The Time Value Of Money

This exercise helps understand how interest rates impact the cost of loans and how they can help save with a savings account! Check how a couple percentage points change the price of things by thousands of dollars & refer to the Saving Vs. Investing Module with any questions.

Question 1

Diane invests $500 that she earned and saved from her job working as a checkout cashier at Target. Her savings account offers her 7% interest.

A. How much will it be worth in 5 years?

B. What about if she waits 10 years?

C. Finally, how much will it be worth in 20 years?

D. How many times would Diane’s $500 double if she waited 20 years?

Question 2

Now Diane finds a new savings account that will give her 10% interest on her $500.

A. How much more will Diane’s account be worth in 5 years with the 10% interest account, than it would be worth with the 7% account?

B. What about after 20 years, using the information from your answer above?

Question 3

Elaine needs to save up $4,000 in 4 years. If she can set aside $1,000 today and find a savings account, what rate of return (or interest rate) does she need on that savings account, to grow her account from $1,000 to $4,000? HINT: She needs to double $1,000 twice to reach $4,000.

Question 4

Frank wants to buy a $10,000 car. The car dealer offers him financing of 60 equal monthly payments, which will include the $10,000 purchase price, plus 9% interest. What will the dollar amount of each of these payments be?

Question 5

With the same information as above, the dealer has also offered to charge 8% interest, but Frank must pay back the loan in 48 equal monthly payments. In this scenario, what will Frank’s payments be?

Teacher Notes

These problems are designed to be worked with a calculator, not solved by mental math, so let students use one. The point is understanding what changes the outcome, principal, rate, and time, not testing arithmetic speed.

Questions 1 and 2 are meant to be worked side by side. Have students keep both sets of answers visible so they can directly compare what a 3-point difference in interest rate does to the same $500 over the same time periods. That comparison is the real lesson, more than any single dollar figure.

Question 3 reverses the direction of the problem. Students are used to solving for an ending balance, so solving for a required rate instead often trips them up at first. The hint about doubling is meant to point students toward reasoning through the problem in steps rather than reaching for a formula they may not have yet.

Questions 4 and 5 shift from saving to borrowing, which is worth calling out explicitly. The same math that grows a savings account also determines what a loan actually costs, and many students don't make that connection on their own.

These problems are one piece of the full Saving vs. Investing unit inside the Rapunzl teacher portal, where activities like this one sit alongside articles, guided practice, and a classroom investing simulator built for grades 6–12.

Get a Rapunzl Demo