Final answer:
The question concerns calculating the present value of an annuity where Jeremy wants to invest an amount to make biannual withdrawals after 7 years at a 4.25% interest compounded monthly. We use the present value of annuity formula with a monthly interest rate and the number of periods to calculate the investment needed.
Step-by-step explanation:
The student asked how much money Jeremy needs to invest in a bank at a 4.25% interest rate compounded monthly to allow for withdrawals of $3,500 at the beginning of every 6 months for 7 years, with the first withdrawal in 7 years. This is a present value of annuity problem due to the periodic withdrawal and compound interest. To calculate this, we can use the present value of annuity formula:
- Determine the interest rate per period. Since the interest is compounded monthly, we divide 4.25% by 12, giving us a monthly rate of 0.3542%.
- Determine the total number of periods. Withdrawals occur every 6 months for 7 years, so there are 14 periods.
- Use the formula P = PMT * [(1 - (1 + r)^(-n))/r], where P is the present value we are trying to find, PMT is the payment amount per period ($3,500), r is the interest rate per period (0.003542), and n is the total number of periods (14).
- Calculate to find P.
After calculating, P gives us the amount of money Jeremy needs to invest today. Note this requires specific financial formulas and might involve the use of a financial calculator or software able to handle annuity present value calculations.