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: Future value compounds a present amount forward; present value discounts a future amount back to today.

Common stuck point: The procedure for present and future value is the easy part; the trap is discounting when you meant to grow (or vice versa). Asking "Am I moving one sum of money forward (growing) or backward (discounting) along the timeline?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I moving one sum of money forward (growing) or backward (discounting) along the timeline?

Worked Examples

Example 1

easy

Find the future value of

\$5{,}000

invested at

4\%

annual interest compounded annually for

6

years.

Answer

\$6{,}326.60

First step

The future value formula for compound interest is

FV = PV \cdot (1 + r)^n

Full solution

2
Substitute: $FV = 5000(1.04)^6$ .
3
$(1.04)^6 \approx 1.2653$ , so $FV \approx 5000 \times 1.2653 = \$6{,}326.60$ .

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

8

years?

Example 3

medium

How much should you invest today at 6% annual compounding to have $5000 in 4 years? Use

1.06^4 = 1.26247696

Example 4

medium

Find the FV of $3000 at 8% annual compounding for 5 years. Use

1.08^5 \approx 1.46933

Example 5

medium

Compute NPV: invest \$1000 today, receive \$600 at year 1 and \$600 at year 2, discount rate 10%.

Example 6

hard

Compute NPV of a project: -$2000 today, +$800 each year for 3 years,

r=8\%

. Use

1.08, 1.1664, 1.259712

Example 7

hard

You invest $1000 at 5% annual compounding. After how many whole years does the balance first exceed $1500? Use

\ln 1.5 \approx 0.4055

\ln 1.05 \approx 0.04879

Example 8

challenge

At an annual rate of 8% compounded annually, what equal annual deposit at the end of each year for 5 years grows to $10000? Use FV-of-annuity factor

((1.08)^5-1)/0.08 \approx 5.8666

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.

Example 3

easy

Find the future value of

100

invested for 1 year at 10% annual interest.

Example 4

easy

Find the present value of

110

received in 1 year at 10% discount rate.

Example 5

easy

What is the future value of

200

in 2 years at 5% annual interest?

Example 6

easy

Find the present value of

121

in 2 years at 10%.

Example 7

easy

Would you rather have

100 today or

100 in 5 years? Why (one reason)?

Example 8

easy

At a 0% interest rate, what is the present value of

500

received in 3 years?

Example 9

easy

Find the future value of

1000

in 1 year at 8%.

Example 10

easy

A project's NPV is positive. Does it earn more or less than the discount rate?

Example 11

medium

Find the future value of

500

in 3 years at 6% compounded annually.

Example 12

medium

Find the present value of

1000

received in 4 years at 5%.

Example 13

medium

Money doubles under 7% annual compounding in about how many years? (Use

(1.07)^{10}\approx1.967

Example 14

medium

Compare:

1000

now vs

1200

in 3 years at 5%. Which is worth more today?

Example 15

medium

Find the future value of

2000

at 6% compounded semiannually for 2 years.

Example 16

medium

What annual rate doubles

100

200

in exactly 8 years if

(1+r)^8=2

and

2^{1/8}\approx1.0905

Example 17

medium

Find the present value of

300

in 1 year plus

300

in 2 years at 10%.

Example 18

medium

An investment costs

900

today and returns

1000

in 1 year. At 5%, find its NPV.

Example 19

medium

Find the present value of

500

received in 2 years at 8%.

Example 20

challenge

How long until

1000

grows to

1500

at 6% annual compounding? Use

\log

and round to two decimals. (

\ln1.5\approx0.405465

\ln1.06\approx0.058269

Example 21

challenge

A bond pays

50

at year 1,

50

at year 2, and

1050

at year 3. At 5%, find its price (present value).

Example 22

challenge

You can invest

5000

today at 7% or receive

7000

in 5 years. Which is better? (

1.07^5\approx1.402552

Example 23

easy

Find the future value of \$1000 invested for 2 years at 10% annual interest, compounded annually.

Example 24

easy

Find the present value of \$200 received in 2 years at a 0% discount rate.

Example 25

easy

Find the future value of \$500 in 1 year at 4% annual interest.

Example 26

easy

Find the present value of \$400 received in 1 year at 25%.

Example 27

easy

Find the future value of $1000 invested for 3 years at 5% annual compounding. Use

1.05^3 = 1.157625

Example 28

medium

Find the future value of $2000 in 4 years at 5% compounded quarterly. Use

(1.0125)^{16} \approx 1.21989

Example 29

medium

Find the present value of $10000 received in 10 years at 6% annual compounding. Use

1.06^{10} \approx 1.79085

Example 30

medium

Using the Rule of 72, estimate how long it takes for money to double at 6% annual compounding.

Example 31

medium

You will receive $1000 in 5 years. Should you accept $700 today if the discount rate is 8%? Use

1.08^5 \approx 1.46933

, so

PV \approx 680.58

Example 32

medium

Find the present value of $200 in 1 year plus $200 in 2 years at 8%. Use

1.08^2 = 1.1664

Example 33

medium

Find the FV of $5000 at 4% compounded semiannually for 3 years. Use

(1.02)^6 \approx 1.12616

Example 34

hard

What annual rate doubles money in 5 years? Use

2^{1/5} \approx 1.14870

Example 35

hard

Find the present value of $100 received in 30 years at 5%. Use

1.05^{30} \approx 4.32194

Example 36

hard

A bond pays $50 yearly for 5 years and $1000 at year 5. At 6%, find its price. Use

1.06^5 \approx 1.33823

, and annuity factor

\sum_{t=1}^5 1.06^{-t}\approx 4.21236

Example 37

hard

You owe $10000 in 3 years. How much should you set aside today at 7% compound interest? Use

1.07^3 \approx 1.22504

Example 38

challenge

Compare continuous compounding to annual compounding. Find FV of $1000 at 5% for 10 years under each. Use

e^{0.5}\approx 1.64872

and

1.05^{10}\approx 1.62889

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Related Concepts

Compound Interest Annuities

Background Knowledge

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

compound interest