Sure, I can definitely help you with that! The formula you're looking for is called the
Future Value of an Annuity with Compounding Interest formula. It looks like this:
Formula:
FV = P * [(1 + r)^n - 1] / r + PMT * [(1 + r)^n - 1] / r
Whe
- FV is the future value of the account
- P is the principal (or starting amount) of the account
- r is the interest rate per period (usually per year)
- n is the number of periods (usually in years)
- PMT is the annual addition to the account
Here's how to use the formula step-by-step:
- Determine the values for P, r, n, and PMT. For example, let's say you have a starting principal of $10,000, an annual interest rate of 5%, a time horizon of 10 years, and you plan to add $1,000 to the account each year.
- Plug those values into the formula:
Formula:
FV = $10,000 * [(1 + 0.05)^10 - 1] / 0.05 + $1,000 * [(1 + 0.05)^10 - 1] / 0.05
- Simplify the formula by calculating the values inside the brackets first:
Formula:
FV = $10,000 * [1.628895 - 1] / 0.05 + $1,000 * [1.628895 - 1] / 0.05
- Simplify further by calculating the values in the parentheses:
Formula:
FV = $10,000 * 32.57789 + $1,000 * 32.57789
- Add those two values together to get the future value of the account:
Formula:
FV = $10,000 * 32.57789 + $1,000 * 32.57789 = $48,778.90
So, in this example, the future value of the account after 10 years with annual additions of $1,000 and an interest rate of 5% would be
$48,778.90.
I hope that helps!