Would appreciate help with learning the formula for how to compound interest
with annual additions. I would like to know the future value of an interest
bearing account starting with a certain principle and adding annual additions
such as one does with a 401K. I know the formula for future value without
additions but not the one including annual additions.

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

1. FV is the future value of the account
2. P is the principal (or starting amount) of the account
3. r is the interest rate per period (usually per year)
4. n is the number of periods (usually in years)
5. PMT is the annual addition to the account

Here's how to use the formula step-by-step:

1. 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.
2. 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 

   
   
3. 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 

   
   
4. Simplify further by calculating the values in the parentheses:
   
   
   Formula:

   FV = $10,000 * 32.57789 + $1,000 * 32.57789 

   
   
5. 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!

The FV() function (future value) will return the future value of a stream of
EQUAL payments and has an optional argument for present value. If you are
going to assume payments of varying amounts, then your best bet is to create
a table with contribution dates and amounts, and apply a compounding formula
to each contribution based on the # of annual periods from the date of
contribution to the "maturity" date. The compounding formula is simply

Contribution amount * (1+int rate)^ (# periods)

So, if A1 contains the contribution amount, and the interest rate is 7.5%,
invested for 15 years, the formula would be

=A1*(1+.075)^15

Compound each of your contributions, then sum all the compounded values.



"charrismd" wrote:

Would appreciate help with learning the formula for how to compound interest
with annual additions. I would like to know the future value of an interest
bearing account starting with a certain principle and adding annual additions
such as one does with a 401K. I know the formula for future value without
additions but not the one including annual additions.