Question

Suppose a lottery prize of $450,000 is placed in account that earns 6.6% interest, compounded monthly. Withdrawals will be made at the beginning of each month for the next 20 years

a) Determine which annuity formula is appropriate for the situation and write it down.
b) Explain why the formula you chose is the appropriate formula.
c) Which quantity in the formula is not given in the information above?
d) Determine how much money can be withdrawn from the account each month.

Answer 1

The appropriate annuity formula for this situation is the future value of an ordinary annuity formula:

`\[ FV = P * \left( ((1 + r)^(nt) - 1)/(r) \right) \]`

Using this formula, the monthly withdrawal amount can be determined.

Step-by-step explanation:

The chosen formula is the future value of an ordinary annuity formula because it calculates the future value of a series of equal payments made at the end of each period, taking into account compound interest. In this scenario, the lottery prize represents the initial deposit, the monthly withdrawals represent the annuity payments, and the interest rate and compounding period are given.

The formula considers the time value of money, accounting for the compounding of interest on the initial deposit over the specified period. In this case, the interest is compounded monthly over 20 years.

The formula allows for the determination of the future value of the annuity, which represents the total amount available in the account after 20 years of monthly withdrawals and compound interest.

The quantity not given in the information is the number of compounding periods per year (n). However, it is mentioned that the interest is compounded monthly, so \(n = 12\).

By plugging in the values for the principal amount, interest rate, time period, and compounding frequency into the formula, one can calculate the monthly withdrawal amount that can be sustained over the 20-year period without depleting the account.