A family raised $1000 for their initial investment. If they invest the money in an account that earns 5% interest compounded ann
ually, what will be the value of their investment at the end of 15 years? The exponential function that expresses the amount of the investment as a function of time when compounded annually is: A(t)=P(1+r)^t
1. Evaluate function: A(15) =
2. Amount of interest earned in dollars:
3. Use the trace function to determine the value of the investment after 18 years.
4. Use the table function to determine how many years it will take for the investment to double.
5. How much more interest would be earned after 15 years if the interest rate were 5.5%?
If the investment is compounded more often than annually, the exponential function becomes ( ) (1 )nt r At P n = + , where n is the number of times the interest is compounded annually. Notice that if n = 1, the formula simplifies to the one used above.
6. If the family’s initial investment is the same with a 5% interest rate, but now it is compounded monthly, what is the value after 15 years of the investment?
7. How many years does it take the investment to double?
8. How much interest would be earned if the initial investment was $1,500 compounded monthly at the same 5% interest rate? How does this compare to the interest earned with the original $1,000 investment?
