PV & FV Calculator — Convert Between Present Value and Future Value
Instantly convert between present value and future value. Select your mode — Find FV or Find PV — enter any 3 variables, and see both values side by side with visual charts and a compounding frequency comparison.
How PV and FV Are Related
Present Value (PV) and Future Value (FV) are two sides of the same coin in the time value of money framework. They are connected by a single mathematical relationship:
Compounding moves money forward in time (PV → FV), while discounting moves it backward (FV → PV). The interest rate r and time period n serve as the bridge between the two.
Think of it this way: if you deposit $10,000 today at 7% for 10 years, it grows to $19,672 (FV). Conversely, $19,672 received in 10 years is only worth $10,000 today (PV) at a 7% discount rate. Same money, same rate, different time perspective.
Converting PV to FV
To convert a present value to a future value, you compound it forward using the interest rate and time period:
Where m is the compounding frequency (1 = annually, 12 = monthly, 365 = daily).
Example: Savings Growth
You invest $25,000 at 8% compounded monthly for 20 years:
Your $25,000 grows to $123,170 — a gain of $98,170 purely from compound interest.
Converting FV to PV
To convert a future value to a present value, you discount it backward:
Example: College Fund Target
You need $200,000 for college in 18 years. At 6% compounded annually:
You need to invest $70,069 today to reach your $200,000 goal.
The Role of Discount Rate & Compounding
The discount rate (or interest rate) is the most influential variable in PV/FV conversions. A small rate change produces dramatic long-term effects:
| $10,000 invested | 5% / 10 yrs | 7% / 10 yrs | 10% / 10 yrs | 7% / 20 yrs | 7% / 30 yrs |
|---|---|---|---|---|---|
| Future Value | $16,289 | $19,672 | $25,937 | $38,697 | $76,123 |
| Interest Earned | $6,289 | $9,672 | $15,937 | $28,697 | $66,123 |
Compounding frequency also matters. More frequent compounding produces a slightly higher effective rate, which accelerates growth and deepens discounts. At 6% for 20 years, annual compounding gives FV = $32,071 while monthly gives FV = $33,102 — a $1,031 difference from the same stated rate.
PV vs FV: When to Use Which
| Use Case | Calculate | Why |
|---|---|---|
| How much will my savings be worth? | FV | Project money forward to see growth |
| How much do I need to invest now? | PV | Find today's amount needed for a future goal |
| Should I take a lump sum or payments? | PV | Compare PV of annuity vs lump sum offer |
| What is this bond worth? | PV | Bond price = PV of all future coupons + face value |
| Retirement projection | FV | How big will my nest egg be at retirement? |
| Compare investment options | Both | Same FV goal → which needs less PV? |
Frequently Asked Questions
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PV and FV are mathematical inverses. FV = PV × (1+r)n compounds money forward, while PV = FV / (1+r)n discounts money backward. They use the same rate and time period to translate value between today and the future.
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Multiply the present value by the compound factor: FV = PV × (1 + r/m)m×n. For example, $10,000 at 6% compounded monthly for 10 years: FV = $10,000 × (1 + 0.005)120 = $18,194.
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Divide the future value by the compound factor: PV = FV / (1 + r/m)m×n. For example, $50,000 in 15 years at 7% annual: PV = $50,000 / (1.07)15 = $18,122. This tells you how much to invest today.
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Yes, especially over long periods. At 6% for 30 years, $10,000 grows to $57,435 with annual compounding but $60,226 with daily compounding — a $2,791 difference. More frequent compounding increases the effective rate, accelerating growth.
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Use FV for forward-looking projections: savings growth, retirement nest egg, investment returns. Use PV for backward-looking valuations: what a future payment is worth today, bond pricing, comparing lump sum vs annuity, NPV analysis.
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The Rule of 72 is a quick mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes for money to double. At 6%, doubling time ≈ 72/6 = 12 years. At 10%, it's about 7.2 years. Works for both PV→FV and FV→PV perspectives.