The time value of money means that money available today is usually worth more than the same amount of money in the future. A dollar today can be spent immediately, saved for emergencies, or invested to earn more money. This idea matters because it helps people compare choices like buying now, saving for college, borrowing, or investing.
It is one of the most important ideas in personal finance and economics.
Key Facts
- Future value with simple interest: FV = P(1 + rt)
- Future value with compound interest: FV = P(1 + r)^t
- Present value formula: PV = FV / (1 + r)^t
- Interest is the price paid for using money over time.
- A higher interest rate makes future value larger and present value smaller.
- Inflation reduces purchasing power, so 1 today.
Vocabulary
- Time Value of Money
- The principle that money available now is worth more than the same amount received later because it can be used or invested.
- Present Value
- The current worth of a future amount of money after accounting for interest or discounting.
- Future Value
- The amount money will grow to after earning interest over time.
- Interest Rate
- The percentage charged or earned for using money during a period of time.
- Inflation
- A general increase in prices that lowers the purchasing power of money.
Common Mistakes to Avoid
- Treating 1 next year as equal, which ignores the chance to earn interest and the effect of inflation.
- Forgetting to convert percentages to decimals, which makes calculations like 5% become 5 instead of 0.05 and gives answers that are far too large.
- Using simple interest when the problem says interest is compounded, which underestimates growth because compound interest earns interest on earlier interest.
- Ignoring the time period of the interest rate, which is wrong because an annual rate, monthly rate, and daily rate do not produce the same result unless adjusted.
Practice Questions
- 1 You invest $100 at 5% annual compound interest for 3 years. Use FV = P(1 + r)^t to find the future value.
- 2 You will receive $500 in 2 years, and the annual discount rate is 4%. Use PV = FV / (1 + r)^t to find its present value.
- 3 A friend offers you 55 one year from now. Explain which option is better if you can earn 8% interest by investing money today.