Final answer:
To determine the annual investment for Cassandra Dawson to reach $12,000 in four years at a 6.8% annual interest rate, the future value of an annuity formula is used, and after plugging in the values and calculating, we can find the required annual investment amount, rounded to the nearest dollar.
Step-by-step explanation:
Calculating the Annual Investment Needed
To calculate the amount Cassandra Dawson needs to invest annually to have $12,000 at the end of four years with an annual interest rate of 6.8%, we can use the formula for the future value of a series of annuities.
The formula for the future value of an annuity is given as:
FV = Pmt * [(1 + r)^n - 1] / r
Where:
- FV is the future value of the annuity, which is $12,000 in Cassandra's case.
- Pmt is the payment amount per period that we want to find out.
- r is the interest rate per period, which is 6.8% or 0.068.
- n is the total number of payments, which is 4 since she will invest at the beginning of each of the next four years.
After rearranging the formula to solve for Pmt, we get:
Pmt = FV / [(1 + r)^n - 1] / r
Plugging in the values, we have:
Pmt = $12,000 / [(1 + 0.068)^4 - 1] / 0.068
Now we calculate the value inside the brackets and then divide $12,000 by this result.
After performing the calculation, we round the result to the nearest dollar to find out how much Cassandra needs to invest annually.