A common component of investing money is to take advantage of a financial institution's willingness to pay compound interest. Compound interest is basically interest paid on a deposit that continually accumulates interest. In general, the formula for compound interest can be represented by the following exponential function:

In this formula, P(t) represents the total money in the account after t years given the interest rate k which is compounded continuously. In this assignment, you will use this formula to explore the affect that compound interest can have over a period of time and at different interest rates.

Directions:

1. Select an amount of money that you would like to invest (for example $1000.00). This will be your P₀ value.
2. Let your interest rate be k = 0.5%.
3. Write out the exponential function using the P₀ and k values you have.
4. Determine the value of your investment after 1, 5, and 10 years.
5. Now, find the doubling time T for your investment. In other words, at what time would your initial deposit double in value?
6. Repeat steps 3 through 5 for k = 1%.
7. Repeat steps 3 through 5 for k = 1.5%.