Calculadora de valor futuro (VF) de una anualidad
Introduction to the Future Value of an Annuity
An annuity, as used here, is a series of regular, periodic payments to or withdrawals from an investment account. Wikipedia lists the following examples of annuities: “regular deposits to a savings account, monthly home mortgage payments, monthly insurance payments, and pension payments.” Annuities can be classified by the frequency of the cash-flow dates. The investor may make deposits, withdrawals, or payments weekly, monthly, quarterly, yearly, or at any other regular interval. This calculator supports 11 frequency options.
The Accurate Future Value of an Annuity Calculator calculates the FV of a series of periodic amounts.
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“What will be the final value of a series of deposits, withdrawals or investments?”
The future value of an annuity is the total amount that the cash flow will be worth on a specified future date. Because the account earns investment gains or interest on the principal, the final value is greater than the sum of the deposits.
This future value of an annuity (FVA) calculator computes the value on any specified future date. You may enter a starting amount that differs from the periodic deposit. This allows you to calculate the FVA of an existing investment.
If the investment is new, set the field “Starting Amount (PV)” to 0.
This FVA calculator can also calculate the future value after a series of withdrawals. For example, if you start with $1,000,000 and assume it earns 4.0% per year, the calculator will compute the value after 30 years of monthly withdrawals of $5,000. To indicate a withdrawal, enter a negative amount.
Future Value of an Annuity-calculate the value of a series of investments or deposits
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Información
Instructions for the Future Value of an Annuity Calculator
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- Starting Amount (PV): The amount of money you have at the beginning of the annuity period. It may be the initial investment or the current value of an existing annuity.
- Periodic Amount: The amount of money you will withdraw (enter a negative value) or contribute (enter a positive value) at regular intervals. The annuity terms determine both the amount and the frequency.
- Number of Periods: The number of times the periodic cash flow will occur.
- Annual Interest Rate: The yearly interest rate the annuity will earn, expressed as a percentage.
- Start Date: The present value date (see note below). This may be the date you purchase the annuity or another predetermined date.
- First Contribution Date: The date of the first contribution or withdrawal from the annuity. This may be the same as the start date or a later date.
- Cash Flow Frequency: How often you will contribute to or withdraw from the annuity. Examples: monthly, quarterly, annually, or another regular interval.
- Monthly Compounding: How often the interest on the annuity is compounded. If you are unsure of the compounding frequency, set this to match the cash flow frequency.
Note: An annuity is a regular cash flow—schedule of contributions or withdrawals. Because this calculator lets you specify both a start date and a first cash flow date that may be different, it can calculate the future value accurately. This remains true even if the cash flows do not begin until years later.
Equations for the Future Value of an Annuity
En esta sección:
Valor futuro de una anualidad ordinaria (con un importe inicial)
For an ordinary annuity, the cash flows occur at the end of each period. To model this, set “First Contribution Date” to any date after “Start Date.” The calculator supports a stub (irregular-length) first period, but the equation does not.
Fig. 2 – Step-by-step solution of the future value of an ordinary annuity equation.
Variables: PV = 32,500; PMT = 525; R = 7.5%; n = 48; f = 12.
Definiciones de variables
- R
- Tipo de interés nominal anual.
- f
- Número de períodos de capitalización por año.
- i
- Tipo de interés periódico.
- PV
- Present value—the starting amount (may be 0).
- PMT
- Periodic cash flow amount. All cash flows are equal.
- n
- Total number of cash flows.
Calculation Steps Explained – Fig. 2
- How do you calculate the future value of an ordinary annuity with a starting amount?
To calculate the future value of an ordinary annuity with a present value (starting amount), use a compound interest equation that accounts for both the initial lump sum and a series of equal payments made at the end of each period. The process is as follows, using these inputs:
PV = 32,500,PMT = 525,n = 48months,R = 7.5%annual interest rate, andf = 12compounding periods per year.- Calculate the periodic interest rate by dividing the nominal annual rate by the number of compounding periods per year:
i = R ÷ f = 0.075 ÷ 12 = 0.00625. - Add 1 to the periodic rate:
1 + i = 1.00625. - Raise the base to the power of the total number of periods:
(1.00625)48 ≈ 1.34859915. - Substitute values into the future value equation:
FV = PV × (1.00625)48 + PMT × [(1.00625)48 − 1] ÷ 0.00625. - Evaluate each part:
32,500 × 1.34859915 ≈ 43,829.47;525 × 55.77586421 ≈ 29,282.33. - Add both parts to calculate the future value:
43,829.47 + 29,282.33 = 73,111.80.
An initial deposit of $32,500 plus 48 monthly payments of $525, invested at a 7.5% annual interest rate compounded monthly, will grow to approximately $73,111.80 at the end of the investment period.
- Calculate the periodic interest rate by dividing the nominal annual rate by the number of compounding periods per year:
Solución paso a paso – Fig. 2
FV = 32,500 × (1.00625)48 + 525 × [(1.00625)48 − 1] ÷ 0.00625≈ 32,500 × 1.34859915 + 525 × (0.34859915 ÷ 0.00625)≈ 32,500 × 1.34859915 + 525 × 55.77586421≈ 43,829.47 + 29,282.33≈ 73,111.80
Respuesta final
The final answer (FV) is approximately 73,111.80.
Validate the calculator. Inputs for a 48-month future value schedule.
| Importe inicial (VP): | 32,500.00 | Periodic Amount (+/−): | 525.00 |
|---|---|---|---|
| Number of Periods: | 48 | Tipo de interés anual: | 7.5% |
| Start Date: | First Contribution Date: | ||
| Cash Flow Frequency: | Mensual | Capitalización: | Mensual |
| Núm./Año | Fecha | Investment | Interés | Cambio neto | Balance/FV |
|---|---|---|---|---|---|
| 47:4 | 525.00 | 444.79 | 969.79 | 72,135.97 | |
| 48:4 | 525.00 | 450.85 | 975.85 | 73,111.82 | |
| 2029 YTD: | 4,200.00 | 3,439.18 | 7,639.18 | ||
| Running Totals: | 57,700.00 | 15,411.82 | |||
| The future value is $0.02 higher than the equation result because the schedule rounds intermediate interest to two decimal places. | |||||
Notas:
- This example uses the same calculation as in Fig. 2.
- If you run this example in this calculator, the future value is 73,111.82. This difference occurs because the calculator generates a monthly schedule and rounds each interest amount to two decimal places, but the closed-form equation does not round intermediate values.
- The starting amount can be 0.
Valor futuro de una anualidad anticipada (con un importe inicial)
For an annuity due, the cash flows occur at the beginning of each period. To model this, set “First Contribution Date” equal to the “Start Date.”
Fig. 4 – Step-by-step solution of the future value of an annuity due equation.
Variables: PV = 32,500; PMT = 525; R = 7.5%; n = 48; f = 12.
Definiciones de variables
- R
- Tipo de interés nominal anual.
- f
- Número de períodos de capitalización por año.
- i
- Tipo de interés periódico.
- PV
- Present value—the starting amount (may be 0).
- PMT
- Periodic cash flow amount. All cash flows are equal.
- n
- Total number of cash flows.
Calculation Steps Explained – Fig. 4
- How do you calculate the future value of an annuity due with a starting amount?
The calculation combines the growth of the initial lump sum with the growth of the annuity-due cash flow stream. The periodic rate is derived from the nominal annual interest rate (APR) and the compounding frequency. Then the values are substituted into the equation and simplified step by step. Approximations are indicated by ellipses.
- Calculate the periodic rate from the nominal APR and compounding frequency:
i = R ÷ f = 0.075 ÷ 12. - Evaluate the periodic rate:
i = 0.00625. - Substitute into the combined future value equation (lump sum plus annuity due):
FV = (32,500 + 525) × (1 + 0.00625)48 + 525 × [((1 + 0.00625)48 − 1 − 1) ÷ 0.00625] × (1 + 0.00625). - Simplify the base while retaining the exponent form:
FV = 33,025 × (1.00625)48 + 525 × [((1.00625)48 − 1 − 1) ÷ 0.00625] × (1.00625). - Approximate the growth factors:
(1.00625)48 ≈ 1.34859915…and(1.00625)47 ≈ 1.34022276…. Update the bracket:FV ≈ 33,025 × 1.34859915… + 525 × [(1.34022276… − 1) ÷ 0.00625] × 1.00625. - Simplify inside the bracket:
FV ≈ 33,025 × 1.34859915… + 525 × (0.34022276… ÷ 0.00625) × 1.00625. - Divide the bracket and retain the timing multiplier:
FV ≈ 33,025 × 1.34859915… + 525 × 54.43564146… × 1.00625. - Compute the lump-sum product and carry the annuity factor:
FV ≈ 44,537.49… + 525 × 54.77586421…. - Multiply the periodic payment by the adjusted factor:
FV ≈ 44,537.49… + 28,757.33…. - Add both parts and round to two decimals:
FV ≈ 73,294.82.
This procedure grows the initial lump sum over all periods and adds the annuity-due cash flow stream with the beginning-of-period timing adjustment.
- Calculate the periodic rate from the nominal APR and compounding frequency:
Solución paso a paso – Fig. 4
i = 0.075 ÷ 12= 0.00625FV = (32,500 + 525) × (1 + 0.00625)48 + 525 × [((1 + 0.00625)48 − 1 − 1) ÷ 0.00625] × (1 + 0.00625)= 33,025 × (1.00625)48 + 525 × [((1.00625)48 − 1 − 1) ÷ 0.00625] × (1.00625)≈ 33,025 × 1.34859915… + 525 × [(1.34022276… − 1) ÷ 0.00625] × 1.00625≈ 33,025 × 1.34859915… + 525 × (0.34022276… ÷ 0.00625) × 1.00625≈ 33,025 × 1.34859915… + 525 × 54.43564146… × 1.00625≈ 44,537.486973… + 525 × 54.77586421…≈ 44,537.49… + 28,757.33…≈ 73,294.82
Respuesta final
The final answer (FV) is approximately 73,294.82 at the end of the 48th period.
Notas:
- For an annuity due, the calculator’s schedule stops at the beginning of the final period. As a result, the schedule output will be lower than the equation result by the amount of interest earned in that final period. This behavior may change in a future update of the calculator.
- The starting amount can be 0.
Future Value of an Annuity Calculator Help
Money—including cash, investments, and receivables—has a different value in the future than it has today. Even cash that does not earn interest will lose value over time. This change in value is called the “future value.”
You must enter either a “Starting Amount” (the cash available at the beginning), a “Regular Contribution Amount”, or both. Set how often you add to the investment by selecting the “Contribution Frequency.” For example, if contributions occur monthly and you enter 120 for “Number of Contributions”, the “Future Value” is calculated for the date that is 10 years after the “First Contribution Date” (120 monthly contributions = 10 years).
Compounding Frequency: Choosing the “Exact/Simple” option means the calculator does not compound interest. It calculates interest for each period using the exact number of days between cash-flow dates. The “Daily” option also uses exact day counts, but it assumes daily compounding (interest is added to principal each day). The “Exact/Simple” setting is the most conservative and produces the lowest future value. Daily compounding produces a higher future value (close to the maximum except for “Continuous Compounding”).
Other compounding frequencies are based on periods longer than one day. Each period is treated as equal in length for interest calculations. For example, if the balance is $10,000, the interest earned for January will equal the interest earned for February, assuming the same annual interest rate.
Note: The future value may be lower than today’s value when inflation is considered. To reflect this, enter a negative interest rate.
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