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What is the Formula for Compound Interest?

What is the formula for compound interest?

Summary

  1. We start with a Principal of $400, and find the money in our account given an annual interest rate of 4%.
  2. In the first year both simple and compound interest earns us $16, because in both cases we're earning 4% on our $400 principal
  3. In the 2nd year with simple interest we earn 4% on the original $400, but with compound interest we earn 4% on the full $416 in our account!
  4. For the same principal, rate, and time, you earn more with compound interest than with simple interest.
  5. We can use the compound interest formula, with t=2, to get the total after 2 years without having to calculate year by year:)

Notes

    1. I- the interest earned
    2. P- the principal, or amount we start with
    3. r- interest rate
    4. t- time
    1. I1- the interest earned in year 1
    2. P- the principal, or amount we start with
    3. r- interest rate
    4. t- time
    5. $400 is our principal investment (P). Interest rate (r) is 4% or 0.04. t = 1 year.
    6. A1 is the money in our account after the first year.
    7. I2- the interest earned in year 2
    8. A2 is the money in our account after the second year.
    9. With simple interest the money earned each year is the same!
    1. So with compound interest you're earning interest on the interest that you make!
    1. I1- the interest earned in year 1
    2. P- the principal, or amount we start with
    3. r- interest rate
    4. t- time
    5. $400 is our principal investment (P). Interest rate (r) is 4% or 0.04. t = 1 year.
    6. A1 is the money in our account after the first year.
    7. The interest in the first year here is the same as when we found simple interest!
    8. I2- the interest earned in year 2
    9. NOTICE!! We plug in A1 instead of P in the 2nd year. This is where compound and simple interest differ!!
    10. A 2 is the money in our account after the second year.
    1. The formula allows you to go straight to the final year instead of calculating each year individually.
    2. A is the money in our account.
    3. P- the principal, or amount we start with
    4. r- interest rate
    5. t- time
    6. We can plug in t = 2 years, our total number of years.
    7. The formula allowed you to go straight to the final year instead of calculating each year individually.