Time Value of Money
The time value of money (TVM) is the concept that money available at the present time is worth more than the identical sum in the future due to its potential earning capacity.
P = A[(1 + i)ⁿ - 1]/[i(1 + i)ⁿ] (Uniform Series Present Worth)
F = A[(1 + i)ⁿ - 1]/i (Uniform Series Future Worth)
Where:
- F = Future value
- P = Present value
- A = Uniform series amount (annuity)
- i = Interest rate per period
- n = Number of periods
Calculation Type
Select what you want to calculate:
Future Value of a Single Payment
Calculate how much a present amount will grow to in the future with compound interest.
Result
Future Value (F):
Present Value of a Single Payment
Calculate what a future amount is worth today (its present value).
Result
Present Value (P):
Present Value of an Annuity
Calculate the present value of a series of equal payments (annuity).
Result
Present Value (P):
Future Value of an Annuity
Calculate the future value of a series of equal payments (annuity).
Result
Future Value (F):
Annuity Payment (Capital Recovery/Sinking Fund)
Calculate the equal payment amount needed to reach a future value (sinking fund) or pay off a present value (capital recovery).
Result
Payment Amount (A):
Practical Examples
Example 1: Future Value of Investment
Invest $10,000 at 5% annual interest for 10 years (compounded annually).
F = 10,000 × (1 + 0.05)¹⁰ = $16,288.95
Example 2: Present Value of Future Sum
How much to invest today to have $50,000 in 8 years at 6% annual interest?
P = 50,000 / (1 + 0.06)⁸ = $31,370.62
Example 3: Annuity Present Value
Value today of 20 annual payments of $5,000 at 7% interest (ordinary annuity).
P = 5,000 × [(1.07)²⁰ - 1]/[0.07(1.07)²⁰] = $52,970.07
Example 4: Sinking Fund Payment
Annual payments needed to accumulate $100,000 in 15 years at 4% interest.
A = 100,000 × 0.04 / [(1.04)¹⁵ - 1] = $4,995.25
Engineering Economics Factors
| Factor | Formula | Notation |
|---|---|---|
| Single Payment Compound Amount | (1 + i)ⁿ | (F/P,i,n) |
| Single Payment Present Worth | 1/(1 + i)ⁿ | (P/F,i,n) |
| Uniform Series Sinking Fund | i/[(1 + i)ⁿ - 1] | (A/F,i,n) |
| Uniform Series Capital Recovery | i(1 + i)ⁿ/[(1 + i)ⁿ - 1] | (A/P,i,n) |
| Uniform Series Compound Amount | [(1 + i)ⁿ - 1]/i | (F/A,i,n) |
| Uniform Series Present Worth | [(1 + i)ⁿ - 1]/[i(1 + i)ⁿ] | (P/A,i,n) |