#### Another View of Future Value

The future value problems we've looked at so far focused on a set amount of money to begin with… $50 in a piggy bank, $5,000 earned from working for a while, a $9,000 bonus by a 25th birthday, and $10,000 from a rich grandma. These were great starting points for saving, but not all of us will have this much to start with or will have some wealthy relative bestow a large sum of cash on us. Most of us will save by depositing small amounts on a regular basis. This can be thought of as an annuity.

It is exciting to watch this type of savings account because it continues to grow, due to the addition of principal (your regular payments) and subsequent interest accumulation.

It might be unrealistic to think you can save $10,000 a year—right now; however, after you complete your education and begin earning a regular paycheck, it will be doable. So, instead of looking at saving $10,000 for 20 years, let's look at saving $10,000 *every year* for 20 years!

Of course, there is a formula for that. The annuity formula assumes the first investment is made at the **end** of the first year, and the last investment is made at the **end** of the last year.

Shown below is the annuity formula and a description of each variable.

FV=(A/ i)[(1+i) ^{n}-1] |
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FV=Future Value
Future value is the amount we don't know. This is the value we will solve for in our calculations. It's the amount we will have in the future. |

A= Annuity
Annuity This is your initial and subsequent payments (which must be the same amount). |

i= interest rate
Interest rate has a great effect on future value. The interest rate in our formula must be written in decimal form: for example, 3% is 0.03. |

n= number of periods
n is the number of equal deposits we will make. |

#### Start With the Variables

How much money will you have in 20 years, if you deposit and save $10,000 *every year *at 3% interest? The first thing we have to do is replace the variables in the equation with the relevant figures in our scenario. Do you know what values to replace A, i, and n with? Enter your answers in the text boxes below. Click Reveal Answer to see if you are correct.

FV=(A/i)[(1 i)^{n}-1]

FV=( / )[(1+ )^{ }-1]

REVEAL ANSWER

#### Now, on to Calculation

OK. Let's walk through the steps of calculating this. Click here to view the demonstration.