Final answer:
Jake Werkheiser's investment of $7,000 annually at a 12% annual compound interest rate for 6 years will be approximately $63,789 at the end of the term, corresponding with answer choice (b).
Step-by-step explanation:
When Jake Werkheiser invests $7,000 annually into an IRA that has a 12% annual compound interest rate, we need to calculate the future value of an annuity due to determine how much he will have at the end of 6 years. This can be calculated using the formula for the future value of an annuity due, which takes into account that contributions are made at the end of each period.
The future value of an annuity due (FV) is given by:
FV = Pmt * [((1 + r)n - 1) / r]
Where Pmt is the annual payment, r is the annual interest rate (as a decimal), and n is the number of periods. For Jake's investment:
- Pmt = $7,000
- r = 0.12
- n = 6
Plugging in the values:
FV = $7,000 * [((1 + 0.12)6 - 1) / 0.12] ≈ $63,789
Therefore, the correct answer to how much Jake will have at the end of the 6 years is approximately $63,789, which corresponds to answer choice (b).