Practice Present and Future Value in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The concept that money has different values at different points in time. Future value (FVFV) calculates what a present amount will grow to; present value (PVPV) 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.

Showing a random 20 of 50 problems.

Example 1

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

Example 2

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

Example 3

hard
A bond pays $50 yearly for 5 years and $1000 at year 5. At 6%, find its price. Use 1.065≈1.338231.06^5 \approx 1.33823, and annuity factor ∑t=151.06−t≈4.21236\sum_{t=1}^5 1.06^{-t}\approx 4.21236.

Example 4

medium
Find the present value of 500500 received in 2 years at 8%.

Example 5

medium
Compare: 10001000 now vs 12001200 in 3 years at 5%. Which is worth more today?

Example 6

medium
What annual rate doubles 100100 to 200200 in exactly 8 years if (1+r)8=2(1+r)^8=2 and 21/8≈1.09052^{1/8}\approx1.0905?

Example 7

medium
Find the future value of 20002000 at 6% compounded semiannually for 2 years.

Example 8

medium
Find the present value of $10000 received in 10 years at 6% annual compounding. Use 1.0610≈1.790851.06^{10} \approx 1.79085.

Example 9

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

Example 10

medium
Find the future value of 500500 in 3 years at 6% compounded annually.

Example 11

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

Example 12

medium
Find the FV of $3000 at 8% annual compounding for 5 years. Use 1.085≈1.469331.08^5 \approx 1.46933.

Example 13

easy
Find the future value of 100100 invested for 1 year at 10% annual interest.

Example 14

medium
Find the present value of 300300 in 1 year plus 300300 in 2 years at 10%.

Example 15

hard
Compare the future values of $10,000\$10{,}000 invested for 2020 years at 6%6\% with (a) annual compounding, (b) monthly compounding, and (c) continuous compounding.

Example 16

easy
Find the present value of 110110 received in 1 year at 10% discount rate.

Example 17

hard
Find the present value of $100 received in 30 years at 5%. Use 1.0530≈4.321941.05^{30} \approx 4.32194.

Example 18

hard
Compute NPV of a project: -$2000 today, +$800 each year for 3 years, r=8%r=8\%. Use 1.08,1.1664,1.2597121.08, 1.1664, 1.259712.

Example 19

easy
Find the future value of $5,000\$5{,}000 invested at 4%4\% annual interest compounded annually for 66 years.

Example 20

easy
What is the future value of 200200 in 2 years at 5% annual interest?
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