Future value of 10,000 at 6% for 10 years
- Solve for
- Future value
- Present value
- 10,000
- Interest rate (per year)
- 6%
- Time
- 10 years
- Compounding
- Yearly
- Future value
- 17,908.48
Checked against: 10000 × 1.06^10 = 17908.4769654…
Time value of money calculator (future and present value)
Solve for the future value, present value, interest rate or time of a lump sum from the other three, with any compounding, including continuous.
By AdminDrafted with AI writing toolsUpdated Checked examples: 9
Future value
$
Future value: $17,908.48
- Effective annual rate
- 6.0000%
- Growth multiple (FV ÷ PV)
- 1.79085
$10,000.00 grows to $17,908.48 in 10 years at 6% a year, 1.791× the starting amount.
Value over time
Value by year
| Year | Start value | Growth | End value |
|---|---|---|---|
| 1 | $10,000.00 | $600.00 | $10,600.00 |
| 2 | $10,600.00 | $636.00 | $11,236.00 |
| 3 | $11,236.00 | $674.16 | $11,910.16 |
| 4 | $11,910.16 | $714.61 | $12,624.77 |
| 5 | $12,624.77 | $757.49 | $13,382.26 |
| 6 | $13,382.26 | $802.94 | $14,185.19 |
| 7 | $14,185.19 | $851.11 | $15,036.30 |
| 8 | $15,036.30 | $902.18 | $15,938.48 |
| 9 | $15,938.48 | $956.31 | $16,894.79 |
| 10 | $16,894.79 | $1,013.69 | $17,908.48 |
How it's calculated S
Grow the present value
Effective annual rate
About the time value of money calculator
The time value of money links four numbers for a single sum: the present value PV, the future value FV, the annual rate r and the time t. With compounding k times a year, FV = PV × (1 + r/k)^(kt), and continuous compounding gives FV = PV × e^(rt). Given any three, the fourth follows: dividing FV by the growth factor gives the present value, a root gives the rate, and logarithms give the time.
With the defaults, 10,000 at 6% compounded yearly grows to 17,908.48 in 10 years, 1.79 times the starting amount. Discounting runs the other way: 20,000 due in 10 years is worth 10,992.65 today at 6% compounded monthly.
This covers one deposit with no further payments; for regular contributions use the compound interest or SIP calculator. The rate is a nominal yearly rate, and the effective annual rate shows what the compounding adds to it.
How to calculate future value and present value
Future value is FV = PV × (1 + r/k)^(kt): the amount today times the growth factor, where r is the nominal annual rate, k the compounding periods a year and t the years. 10,000 at 6% compounded yearly grows to 17,908.48 in 10 years. Present value divides instead: PV = FV ÷ (1 + r/k)^(kt).
Discounting answers what a future sum is worth today. At 6% compounded monthly, 20,000 due in ten years is worth 20,000 ÷ 1.005^120 = 10,992.65 now.
These formulas cover one sum and one future value at a constant rate, with nothing paid in or taken out between them. Continuous compounding replaces the growth factor with e^(rt).
Future value worked by hand
For 10,000 at 6% compounded monthly for ten years:
- Rate per period: 0.06 ÷ 12 = 0.005, so the monthly factor is 1.005.
- Number of periods: 12 × 10 = 120.
- Future value: 10,000 × 1.005^120 = 18,193.97.
The 6% is a yearly nominal rate. A 6% monthly rate would be a different problem with a far larger answer.
The calculation is the zero-payment case of Microsoft Excel's FV function: =FV(6%/12, 120, 0, -10000) returns 18,193.97. The present value is entered as negative because it is money paid out.
How to calculate the interest rate needed
For periodic compounding, r = k × ((FV ÷ PV)^(1 ÷ kt) − 1); for continuous compounding, r = ln(FV ÷ PV) ÷ t. Doubling 10,000 to 20,000 in ten years with yearly compounding takes 2^(1/10) − 1 = 7.1773% a year.
The nominal rate you need depends on the compounding, but the effective annual rate, (1 + r/k)^k − 1 or e^r − 1, stays the same. Every row below doubles 10,000 in ten years:
| Compounding | Required nominal annual rate | Effective annual rate |
|---|---|---|
| Yearly | 7.1773% | 7.1773% |
| Half-yearly | 7.0530% | 7.1773% |
| Quarterly | 6.9919% | 7.1773% |
| Monthly | 6.9515% | 7.1773% |
| Daily (365) | 6.9321% | 7.1773% |
| Continuous | 6.9315% | 7.1773% |
Excel's RRI function computes the same per-period root. If its periods are months, the answer is a monthly rate, so convert it before calling it a yearly one.
The same formula recovers a cumulative fixed deposit's rate, as long as the interest stays reinvested and you know how often it compounds.
A deposit of 100,000 that matures at 141,477.82 after 5 years, compounded quarterly, earned 4 × (1.4147782^(1/20) − 1) = 7.00% a year.
A future value below the present value gives a negative rate: 10,000 falling to 8,000 over ten years is −2.2067% a year.
How long it takes to reach a target
t = ln(FV ÷ PV) ÷ (k × ln(1 + r/k)), or ln(FV ÷ PV) ÷ r with continuous compounding. Doubling at 7% compounded monthly takes ln 2 ÷ (12 × ln(1 + 0.07/12)) = 9.93 years, or 119.17 monthly periods.
Excel's PDURATION function counts the same periods. A fractional period is a mathematical answer: an account that credits interest only on set dates reaches the target at the next crediting date.
The table grows 10,000 and discounts 20,000 over ten years at 6%, then solves the time to double at 7%. Amounts and years are rounded to two decimals:
| Compounding | 10000 grown for 10 years at 6% | PV of 20000 in 10 years at 6% | Years to double at 7% |
|---|---|---|---|
| Yearly | 17908.48 | 11167.90 | 10.24 |
| Half-yearly | 18061.11 | 11073.52 | 10.07 |
| Quarterly | 18140.18 | 11025.25 | 9.99 |
| Monthly | 18193.97 | 10992.65 | 9.93 |
| Daily (365) | 18220.29 | 10976.77 | 9.90 |
| Continuous | 18221.19 | 10976.23 | 9.90 |
Daily (365) means exactly 365 periods a year, which may differ from a bank's day-count convention and payment dates.
When there is no answer
- Zero rate. The value never changes, so a different target is never reached, and an equal target has no single waiting time.
- A lower target at a positive rate. Growth only moves the value up, so a positive rate cannot reach a smaller amount.
- Equal values. The rate needed is zero.
Mistakes to avoid
- Treating a loan's total repayments as a future value. An installment loan repays principal every month, so a lump-sum rate understates its true rate. Use the EMI calculator for reducing-balance loans.
- Comparing nominal rates with different compounding. Compare the effective annual rates instead.
- Ignoring deposits along the way. Regular contributions need the compound interest calculator, and dated cash flows need the XIRR calculator.
The ROI and CAGR calculator reports effective annualized growth between two values. Nothing here deducts inflation, taxes or fees.
Worked examples
Present value of 20,000 in 10 years at 6% monthly
- Solve for
- Present value
- Future value
- 20,000
- Interest rate (per year)
- 6%
- Time
- 10 years
- Compounding
- Monthly
- Present value
- 10,992.65
- Effective annual rate
- 6.1678%
Checked against: 20000 / 1.005^120 = 10992.6546672…
Excel RRI: 10,000 to 11,000 over 96 months
- Solve for
- Rate
- Present value
- 10,000
- Future value
- 11,000
- Time
- 8 years
- Compounding
- Monthly
- Interest rate needed (per year)
- 1.1920%
Checked against: Microsoft RRI documentation: =RRI(96,10000,11000) = 0.0009933 per month; × 12 = 1.19197 %
Excel PDURATION: 2,000 to 2,200 at 2.5%
- Solve for
- Time
- Present value
- 2000
- Future value
- 2200
- Interest rate (per year)
- 2.5%
- Compounding
- Yearly
- Time needed
- 3.86 years
Checked against: Microsoft PDURATION documentation: =PDURATION(2.5%,2000,2200) = 3.86 years; ln 1.1 / ln 1.025 = 3.85987
Questions
How do you calculate the future value of a lump sum?
Multiply the present value by (1 + r/k)^(kt), where r is the annual rate, k the compounding periods a year and t the years. 10,000 at 6% compounded yearly for 10 years grows to 10,000 × 1.06^10 = 17,908.48. Excel's =FV(6%, 10, 0, -10000) returns the same amount.
How do you calculate present value?
Divide the future amount by the growth factor: PV = FV ÷ (1 + r/k)^(kt). At 6% compounded monthly, 20,000 due in 10 years is worth 20,000 ÷ 1.005^120 = 10,992.65 today. A higher discount rate or a longer wait lowers the present value; Excel's =PV(0.5%, 120, 0, -20000) gives the same figure.
How do you work out the interest rate needed to reach a target?
Take the growth multiple to the power 1 ÷ (number of periods) and subtract 1: r = (FV ÷ PV)^(1/t) − 1. Doubling money in 10 years takes 2^(1/10) − 1 = 7.18% a year. Microsoft's example for Excel's RRI function, 10,000 growing to 11,000 over 96 months, gives 0.0009933 a month, 1.19% a year.
How long does it take for money to reach a target amount?
Divide the logarithm of the growth multiple by the logarithm of one plus the rate per period: n = ln(FV ÷ PV) ÷ ln(1 + r/k). Growing 2,000 to 2,200 at 2.5% a year takes ln 1.1 ÷ ln 1.025 = 3.86 years, the answer Excel's PDURATION function gives. Doubling at 7% compounded monthly takes 119.17 months, or 9.93 years.
What is the difference between a nominal and an effective annual rate?
The nominal rate is the quoted yearly rate; the effective rate includes interest earned on interest within the year: (1 + r/k)^k − 1. A nominal 6% compounded monthly is 6.1678% effective, 6.1831% compounded daily and 6.1837% compounded continuously (e^0.06 − 1). Compare offers on the effective rate, not the nominal one.
About this calculator
Sources
- Microsoft Excel RRI function
- Microsoft Excel PDURATION function
- Brealey, Myers & Allen — Principles of Corporate Finance, ch. 2 (present values)
For planning only. Lenders, tax authorities and markets apply their own rounding, fees and rules; confirm figures with them before you commit.
Checked against references
This calculator includes 9 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.