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]|
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.
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=( / )[(1+ ) -1]
FV=(10,000/.03)[(1+ .03)20 -1]
Do your values match ours? 10,000 is the annuity because it is the amount of our regular payments. 3% is our interest rate, so we write this as .03. (If you mistakenly input "3" instead of ".03," don't worry about it; just keep this in mind for future calculations.) Finally n=20 because n represents the number of years we plan to save and the number of deposits we plan to make.
Now, on to Calculation
OK. Let's walk through the steps of calculating this. Click here to view the demonstration.