How can I calculate my savings with varying deposits using the interest formula?

[Unassuming]

Homework Statement

Using the following savings formula, where d is a uniform deposit, i= (interest rate)/(# times compounded per year), n is the total times compounded.

As I understand it, this formula will tell me how much I will have after depositing a certain amount of money per compounding period given an interest rate and time.

How can I take into account the situation where I start off by depositing a large sum like $5000, and then make uniform deposit during every compounding period?

Homework Equations

I am using the savings formula,

[tex]A=d(\frac{(1+i)^n-1}{i})[/tex]

The Attempt at a Solution

 

[HallsofIvy]

Use that formula one the first amount, the same formula, with the time one month less, on the amount deposited for the second month, the formula with the time two months less for the amount deposited on the third month, etc. and then add them all.

 

[Architeuthis Dux]

To calculate your savings with varying deposits using the interest formula, you can follow these steps:

1. Determine the interest rate and the number of times the interest is compounded per year (i and n in the formula).
2. Decide on a uniform deposit amount (d) that you will make during each compounding period.
3. Calculate the total number of compounding periods (n) based on the length of time you will be saving for.
4. Use the formula A=d(\frac{(1+i)^n-1}{i}) to calculate the total amount you will have after the first compounding period, assuming you start with a large initial deposit (such as $5000).
5. For each subsequent compounding period, use the formula A=d(\frac{(1+i)^n-1}{i}) again, but this time, use the previous period's total amount as the new initial deposit.
6. Repeat this process for each compounding period until you have reached the end of your savings period.
7. Add up all of the amounts calculated in each compounding period to determine your total savings after the specified time frame.

Alternatively, you can use a financial calculator or an online savings calculator that takes into account varying deposits and compounding periods to make the calculation process easier. Remember to also consider any fees or taxes that may affect your savings.