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- 1 future value of 1

# future value of 1

## What is the 'Future Value Of An Annuity'

The future value of an annuity is the value of a group of recurring payments at a specified date in the future; these regularly recurring payments are known as an annuity. The future value of an annuity measures how much you would have in the future given a specified rate of return or discount rate. The future cash flows of the annuity grow at the stated discount rate, so a higher discount rate results in a higher future value for the annuity.

## BREAKING DOWN 'Future Value Of An Annuity'

Because of the time value of money, cash flows received today are worth more than the same cash flows in the future. The money received today can be invested now and grow over time. By the same logic, receiving $5,000 today is worth more than getting $1,000 per year for five years. The lump sum invested today is worth more at the end of the five years than the incremental investments of $1,000 each, even if they are invested at the exact same interest rate.

## Ordinary Annuity Present Value Example Calculation

The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:

P = PMT x (((1 + r) ^ n - 1) / r)

P = the future value of an annuity stream

PMT = the dollar amount of each annuity payment

r = the interest rate (also known as the discount rate)

n = the number of periods in which payments will be made

Assume a portfolio manager decides to invest $125,000 per year for the next five years into an investment that he expects to compound at 8% per year. The expected future value of this payment stream using the above formula is:

Future value of annuity = $125,000 x (((1 + 0.08) ^ 5 - 1) / 0.08) = $733,325

This formula is for the future value of an ordinary annuity where payments are made at the end of the period in question. With an annuity due, the payments are made at the beginning of the period in question. To find the future value of an annuity due, simply multiply the above formula by a factor of (1 + r):

P = PMT x (((1 + r) ^ n - 1) / r) x (1 + r)

If the above example was actually an annuity due, its future value would be calculated as:

Future value of annuity due = $125,000 x (((1 + 0.08) ^ 5 - 1) / 0.08) x (1 + 0.08) = $791,991.

The future value of a sum of money invested at interest rate *i* for one year is given by:

FV = future value

PV = present value

*i* = annual interest rate

If the resulting principal and interest are re-invested a second year at the same interest rate, the future value is given by:

In general, the future value of a sum of money invested for *t* years with the interest credited and re-invested at the end of each year is:

#### Solving for Required Interest Rate or Time

Given a present sum of money and a desired future value, one can determine either the interest rate required to attain the future value given the time span, or the time required to reach the future value at a given interest rate. Because solving for the interest rate or time is slightly more difficult than solving for future value, there are a few methods for arriving at a solution:

Iteration - by calculating the future value for different values of interest rate or time, one gradually can converge on the solution.

Financial calculator or spreadsheet - use built-in functions to instantly calculate the solution.

Interest rate table - by using a table such as the one at the end of this page, one quickly can find a value of interest rate or time that is close to the solution.

Algebraic solution - mathematically calculating the exact solution.

Beginning with the future value equation and given a fixed time period, one can solve for the required interest rate as follows.

Dividing each side by *PV* and raising each side to the power of 1/*t*:

The required interest rate then is given by:

To solve for the required time to reach a future value at a specified interest rate, again start with the equation for future value:

Taking the logarithm (natural log or common log) of each side:

Relying on the properties of logarithms, the expression can be rearranged as follows:

### 3 Comments on Future value of $1 table

Sir, I want to know how you calculate 2.813* ? as per your solution of compound Interest

waiting your prompt Reply

(1.09)raise to the power 12 = 2.813

alternatively multiply (1.09)x(1.09)x(1.09)x(1.09)x(1.09)x(1.09)x(1.09)x(1.09)x(1.09)x(1.09)x(1.09)x(1.09)=2.813

## Future Value of $1 Table Creator

where FV is the future value, PV is the present value = $1, i is the interest rate in decimal form and n is the period number. PV is the Present Value (Principal amount of money = $1) to be invested at an Interest Rate per period for n Number of Time Periods to grow to FV.

You can then look up FV in the table and use this value as a factor in calculating the future value of an investment amount.

Since PV = 1 the FV is the Future Value Interest Factor (FVIF).

**Future value table example with annual compounding:** You want to invest $10,000 at an annual interest rate of 5.25% that compounds annually for 15 years. What will be the value of your account at the end of 15 years?

- Create a table that includes i = 5.25% and n = 15
- Look up FV to find 2.15443
- Use it as a factor to calculate $10,000 * 2.15443 = $21,544.30 which is the value of your investment, future value, after 15 years.

**Future value table example with monthly compounding:** You want to invest $10,000 at an annual interest rate of 5.25% that compounds monthly for 15 years. What will be the value of your account at the end of 15 years?

In this example you must convert periods and the interest rate to months since that is the base period for compounding. 15 years * 12 = 180 months and 5.25%/year divided by 12 = 0.4375%/month.

- Create a table that includes i = 0.4375% and n = 180
- Look up FV to find 2.19412
- Use it as a factor to calculate $10,000 * 2.19412 = $21,941.20 which is the value of your investment, future value, after 15 years. Since compounding is occurring more often the ending value is greater than the future value of the annually compounding example.

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