What is the Time Value of Money?
The time value of money is a core principle in finance: a dollar today is worth more than a dollar in the future because money can earn interest. This concept drives all investment, loan, and savings decisions.
TVM means money grows (or shrinks) over time due to interest. The future value (FV) of a present sum is FV = PV × (1+r)^n, where r is the interest rate and n is the number of periods. Conversely, PV = FV / (1+r)^n.
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Step-by-step worked examples
If you invest $5,000 today at 6% annual interest, how much will it grow in 3 years?
FV = PV × (1 + r)^n FV = $5,000 × (1 + 0.06)^3 FV = $5,000 × (1.06)^3 FV = $5,000 × 1.1910 FV = $5,955
You need $20,000 in 5 years. If the bank offers 4% annual interest, how much must you deposit today (present value)?
PV = FV / (1 + r)^n PV = $20,000 / (1.04)^5 PV = $20,000 / 1.2167 PV = $16,438.54
A retirement account grows from $50,000 to $100,000 over 10 years. What was the average annual return (interest rate)?
$100,000 = $50,000 × (1 + r)^10 2 = (1 + r)^10 r = 2^(1/10) − 1 = 1.0718 − 1 = 0.0718 = 7.18% annual return
Flashcards
Quick quiz
Q1.$1,000 invested at 5% annual rate for 2 years becomes…
Q2.You want $10,000 in 5 years at 8% annual interest. Present value needed is…
Q3.Doubling your money at 10% annual rate takes approximately how many years?
Q4.If inflation is 3% and your savings earn 2% interest, your real return is…
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Common mistakes
Using simple interest instead of compound interest. — Correct: Money grows via compound interest: FV = PV × (1+r)^n, not PV × (1 + r×n).
Ignoring the rate of return when comparing investment choices. — Correct: A higher rate (6% vs. 3%) dramatically changes future value; always factor in the return.
Thinking nominal interest equals real return. — Correct: Real return = nominal rate − inflation. A 5% return in 8% inflation = −3% real return.
Confusing FV and PV calculations. — Correct: FV = PV × (1+r)^n (growth). PV = FV / (1+r)^n (discount). They are inverses.
FAQ
What is time value of money with example?
$1,000 today at 5% annual interest becomes $1,050 in one year. So $1,000 now = $1,050 in one year, at 5% rate.
Why is money worth more today than tomorrow?
Money today can be invested and earn interest; it has more earning potential. Also, inflation erodes future purchasing power.
What is the difference between present value and future value?
Present value is what today's amount is worth now. Future value is what it will grow to. FV = PV × (1+r)^n.
How does compound interest relate to time value of money?
Compound interest is the mechanism behind TVM—interest earned gets reinvested, earning interest itself, making money grow exponentially.