Compound Interest With Deposits

Do you want to know how your credit card bill eats your money when you don't pay? Or how to estimate the amount of money you will receive in your savings account? If you have ever been curious about how those online compound interest calculators work, this is the video for you.

I derive the formula for the total yield for compound interest with the addition of deposits. This formula assumes interest is going to be paid at the beginning of the year, so January 1st for example, while the deposits will occur at the end of each month (or once a year). Using a year as the compounding frequency is arbitrary; you can use this to understand monthly compounding as well, as long as you account for it in the rate of return - meaning an interest rate of 5% per year will need to be divided by the number of compounding periods (monthly would be 5%/12 months = 0.00417 = r). The construction of this formula yields what you would have at the end of the year after all monthly deposits, but before the next interest cycle. To change this, you just subtract the deposits (P in this formula) to see what you would have at the beginning of the year right after you receive interest.

This is a video in the Math of Finance Category, specifically the compound interest group. Subscribe to learn how math applies to everyday life, not just finance and investing but biology, physics, gambling, and so much more!

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{ MathHead }