Question

Your non-profit organization is given a gift of $38,000 to cover your annual healthcare costs for the next 5 years. If your bank presents you with an option for a 6% nominal interest rate compounded monthly, how much can you withdraw each year if you're withdrawing equal yearly sums?

Answer 1

To withdraw equal yearly sums, the amount you can withdraw each year is approximately $9,021.88.

Step-by-step explanation:

To calculate the amount that can be withdrawn each year, we need to consider the bank's interest rate and the number of years. The formula to calculate the equal yearly sums is:

Withdrawal Amount = Principal Amount / Annuity Factor

The principal amount is $38,000, and the interest rate is 6% compounded monthly. The annuity factor can be calculated using the formula:

Annuity Factor = (1 - (1 + r)^(-n))/r

Plugging in the values:

Annuity Factor = (1 - (1 + 0.06/12)^(12*5))/(0.06/12)

Using a calculator, the annuity factor is approximately 4.21299.

Dividing the principal amount by the annuity factor:

Withdrawal Amount = $38,000 / 4.21299 = $9,021.88 (rounded to the nearest cent).