Present and Future Value Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Present and Future Value.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The concept that money has different values at different points in time. Future value (FV) calculates what a present amount will grow to; present value (PV) calculates what a future amount is worth today, using discounting.

Would you rather have \100 today or \100 in five years? Today, obviously—because you could invest the \100 and have MORE than \100 in five years. Present value answers: 'How much would I need TODAY to have \X in the future?' Future value answers: 'If I invest \X today, what will it become?' Discounting is the reverse of compounding—it shrinks future money back to today's value.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Money today is worth more than the same amount in the future because of its earning potential. Discounting converts future cash flows to present-day equivalents, enabling fair comparison of money received at different times.

Common stuck point: The discount rate r is the opportunity cost—what you could earn elsewhere. A higher discount rate makes future money worth LESS today, because your alternative investment would grow faster.

Sense of Study hint: Ask: am I moving money forward in time (use FV = PV*(1+r)^t) or backward (use PV = FV/(1+r)^t)? Draw a timeline to clarify.

Worked Examples

Example 1

easy
Find the future value of \5{,}000 invested at 4\% annual interest compounded annually for 6$ years.

Solution

  1. 1
    The future value formula for compound interest is FV = PV \cdot (1 + r)^n.
  2. 2
    Substitute: FV = 5000(1.04)^6.
  3. 3
    (1.04)^6 \approx 1.2653, so FV \approx 5000 \times 1.2653 = \6{,}326.60$.

Answer

\$6{,}326.60
Future value tells you how much a present sum will be worth after earning compound interest. The formula FV = PV(1+r)^n assumes interest is reinvested (compounded). The interest earned is \1{,}326.60 — more than simple interest (\1{,}200) because of compounding.

Example 2

medium
How much should you invest today at 5\% annual interest compounded quarterly to have \20{,}000 in 8$ years?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
An investment doubles in 9 years with annual compounding. What is the approximate annual interest rate?

Example 2

hard
Compare the future values of \10{,}000 invested for 20 years at 6\%$ with (a) annual compounding, (b) monthly compounding, and (c) continuous compounding.
← Back to Present and Future Value Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

compound interest