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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.

更新日 検証済みの例：9

$
%
years
試す
Future value
$
Future value: $17,908.48
小数点以下の桁数：2；最も近い値へ、等距離なら末尾が偶数の値へ
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

$10K$12K$14K$16K0246810YearsPVFV
Value by year 行数：10
年Start valueGrowthEnd 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
計算方法 S

  1. Grow the present value

    FV=PV×(1+0.061)1×10=10,000.00×1.790847697=17,908.48FV = PV \times \left(1+\frac{0.06}{1}\right)^{1 \times 10} = 10{,}000.00 \times 1.790847697 = 17{,}908.48

  2. Effective annual rate

    (1+r1)1−1=6.0000%\left(1+\frac{r}{1}\right)^{1} - 1 = 6.0000\%

Time value of money calculator (future and present value)について

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.

計算例

Future value of 10,000 at 6% for 10 years

Solve for
Future value
Present value
10,000
Interest rate (per year)
6%
時間
10 years
Compounding
Yearly
Future value
17,908.48

照合元：10000 × 1.06^10 = 17908.4769654… (Python decimal)

Present value of 20,000 in 10 years at 6% monthly

Solve for
Present value
Future value
20,000
Interest rate (per year)
6%
時間
10 years
Compounding
Monthly
Present value
10,992.65
Effective annual rate
6.1678%

照合元：20000 / 1.005^120 = 10992.6546672… (Python decimal)

Excel RRI: 10,000 to 11,000 over 96 months

Solve for
Rate
Present value
10,000
Future value
11,000
時間
8 years
Compounding
Monthly
Interest rate needed (per year)
1.1920%

照合元：Microsoft RRI documentation: =RRI(96,10000,11000) = 0.0009933 per month; × 12 = 1.19197 % (Python decimal 12·(1.1^(1/96) − 1))

Excel PDURATION: 2,000 to 2,200 at 2.5%

Solve for
時間
Present value
2000
Future value
2200
Interest rate (per year)
2.5%
Compounding
Yearly
Time needed
3.86 years

照合元：Microsoft PDURATION documentation: =PDURATION(2.5%,2000,2200) = 3.86 years; ln 1.1 / ln 1.025 = 3.85987 (Python decimal)

よくある質問

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.

「Time value of money calculator (future and present value)」の精度はどのくらいですか？

精度は入力値と計算方法の前提に依存します。十進演算には有効数字50桁を使いますが、推定、数値計算手法、元データの精度はそれより低い場合があります。表示の丸め処理でこれらの制約がなくなるわけではありません。 独立した出典の解答と照合した計算例：9。 例えば、「Future value of 10,000 at 6% for 10 years」は10000 × 1.06^10 = 17908.4769654… (Python decimal)と照合しています。

この計算方法の出典は何ですか？

Microsoft Excel RRI function; Microsoft Excel PDURATION function; Brealey, Myers & Allen — Principles of Corporate Finance, ch. 2 (present values).

この計算機について

FV=PV(1+rk)kt  (continuous: PVert),r=k[(FV/PV)1/(kt)−1],t=ln⁡(FV/PV)kln⁡(1+r/k)FV = PV\left(1+\tfrac{r}{k}\right)^{kt}\ \ (\text{continuous: } PV e^{rt}),\quad r = k\left[(FV/PV)^{1/(kt)} - 1\right],\quad t = \frac{\ln(FV/PV)}{k \ln(1+r/k)}

出典

  1. Microsoft Excel RRI function
  2. Microsoft Excel PDURATION function
  3. Brealey, Myers & Allen — Principles of Corporate Finance, ch. 2 (present values)

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出典と照合済み

この計算機には、独立した出典の解答を使った計算例が 9 件あります。テストに組み込まれており、ここでも実行できます。

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