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.
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≈1.33823, and annuity factor ∑t=151.06−t≈4.21236.
Example 4
medium
Find the present value of 500 received in 2 years at 8%.
Example 5
medium
Compare: 1000 now vs 1200 in 3 years at 5%. Which is worth more today?
Example 6
medium
What annual rate doubles 100 to 200 in exactly 8 years if (1+r)8=2 and 21/8≈1.0905?
Example 7
medium
Find the future value of 2000 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≈1.79085.
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.
Example 10
medium
Find the future value of 500 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≈1.46933.
Example 13
easy
Find the future value of 100 invested for 1 year at 10% annual interest.
Example 14
medium
Find the present value of 300 in 1 year plus 300 in 2 years at 10%.
Example 15
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 16
easy
Find the present value of 110 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≈4.32194.
Example 18
hard
Compute NPV of a project: -$2000 today, +$800 each year for 3 years, r=8%. Use 1.08,1.1664,1.259712.
Example 19
easy
Find the future value of $5,000 invested at 4% annual interest compounded annually for 6 years.
Example 20
easy
What is the future value of 200 in 2 years at 5% annual interest?