Lesson 45 - The Time Value of Money
Money today is more valuable than the same money tomorrow. This idea is called the time value of money (TVM). A euro now can earn returns, protect against inflation, and keep options open. Waiting reduces its power.
Why time changes value
Four reasons explain TVM. Opportunity cost - money now can be invested. Inflation - rising prices shrink future buying power. Risk - future cash may never arrive. Time preference - people usually prefer resources sooner. These forces lower the value of delayed payments.
Core formulas
Future Value:
FV = PV × (1 + r)^nPresent Value:
PV = FV ÷ (1 + r)^nExample: €1,000 at 5% for 3 years grows to €1,158. If you are offered €1,158 in 3 years and use a 5% discount rate, it equals €1,000 today.
Story: Anna’s car fund
Anna, 21, wants to buy a car in 2 years. She can either keep €8,000 in cash or invest it at 4%. If she invests, the fund will reach about €8,659. If she waits with cash, inflation of 3% per year means her €8,000 will buy goods worth only €7,520 in today’s money. By understanding TVM, Anna sees that investing even at modest rates protects her car budget from losing value.
Mini-study: How discounting is used
Families apply TVM when deciding between lump sum or monthly payments. Businesses use discount rates to decide if projects are worth it. Governments use it to value bonds. The higher the risk, the higher the discount rate, and the lower the present value of future cash flows.
Graph: Growth of €1,000
Compounding makes small interest differences huge over time.
Table: Future value of €1,000
Summary
- Money today is more valuable than the same money in the future.
- TVM uses FV and PV to compare options fairly.
- Small rate gaps turn into big value gaps as years pass.
Key Terms
Further Learning
Track Progress
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