What is Future Value?
Future value (FV) shows how much a sum of money invested today will grow to after earning compound interest over time. It's the mirror image of present value and is central to savings, investment, and retirement planning.
Future value is the amount a present sum grows to after compounding at a given rate over a number of periods: FV = PV × (1 + r)^n.
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Step-by-step worked examples
If you invest $1,000 today at a 6% annual interest rate, what is it worth in 10 years?
FV = PV × (1+r)^n FV = 1,000 × (1.06)^10 FV = 1,000 × 1.79085 FV ≈ $1,790.85
You deposit $5,000 at a 4% annual rate for 15 years. Find the future value.
FV = 5,000 × (1.04)^15 FV = 5,000 × 1.80094 FV ≈ $9,004.72
An investment of $2,000 grows at 10% per year for 8 years.
FV = 2,000 × (1.10)^8 FV = 2,000 × 2.14359 FV ≈ $4,287.18
Flashcards
Quick quiz
Q1.What is the future value of $1,000 invested for 1 year at 10%?
Q2.In FV = PV(1+r)^n, what does n represent?
Q3.As the number of years increases (rate fixed), future value…
Q4.$1,000 at 5% for 2 years compounded annually equals…
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Common mistakes
Using simple interest instead of compound interest for FV. — Correct: FV uses compound growth: FV = PV(1+r)^n, not PV(1+r×n).
Forgetting to convert the interest rate to a decimal. — Correct: Convert percentages to decimals (6% = 0.06) before applying the formula.
Mixing up FV and PV in the formula. — Correct: FV is the larger, later amount; PV is the smaller, earlier amount — FV = PV × growth factor.
Assuming FV grows linearly with time. — Correct: FV grows exponentially due to compounding, not in a straight line.
FAQ
What is future value?
Future value is what a sum of money today will be worth after compounding at a given interest rate over time: FV = PV×(1+r)^n.
What is the future value formula?
FV = PV × (1 + r)^n, where PV is the initial amount, r is the interest rate, and n is the number of periods.
How do you calculate future value?
Multiply the present value by (1 plus the interest rate) raised to the number of periods: FV = PV×(1+r)^n.
What are examples of future value in real life?
Projecting a savings account balance, estimating retirement fund growth, or forecasting the maturity value of a fixed deposit.