Question 1191378: You deposit $500 each month into an account earning 2% interest compounded monthly.
a) How much will you have in the account in 20 years?
b) How much total money will you put into the account?
c) How much total interest will you earn?
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's how to break down this savings calculation:
**a) Future Value:**
To figure out how much you'll have in 20 years, we need to use the future value of an ordinary annuity formula. This formula takes into account both your regular contributions and the compounding interest.
* **The Formula:** FV = P * [((1 + r)^n - 1) / r]
Where:
* FV = Future Value (what we want to find)
* P = Periodic Payment ($500)
* r = Interest rate per period (2% per year / 12 months = 0.02/12)
* n = Number of periods (20 years * 12 months = 240 months)
* **Calculation:** FV = 500 * [((1 + 0.02/12)^240 - 1) / (0.02/12)]
FV = 500 * [(1.4907 - 1) / 0.001667]
FV = 500 * [0.4907 / 0.001667]
FV ≈ $147,398.42
**b) Total Deposits:**
This is a simple calculation. You're depositing $500 each month for 20 years.
* **Calculation:** Total Deposits = $500 * 240 months = $120,000
**c) Total Interest Earned:**
The interest earned is the difference between your future value and the total amount you deposited.
* **Calculation:** Total Interest = $147,398.42 - $120,000 = $27,398.42
**Summary:**
* **a) Future Value:** You will have approximately $147,398.42 in the account after 20 years.
* **b) Total Deposits:** You will have deposited a total of $120,000.
* **c) Total Interest:** You will have earned approximately $27,398.42 in interest.
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