Question

How long will $570,000, in an investment account that earns 4.25% compounded monthly, sustain month-end withdrawals of $3,800? (Do not round intermediate calculations and round up the number of payments, n, to the next whole number.)

Answer 1

To determine how long $570,000 will sustain monthly withdrawals of $3,800 with a 4.25% interest rate compounded monthly, we need to solve for the number of payments, n. After solving the equation, we find that n is approximately 157.4, rounding up to 158. Therefore, the money will sustain the withdrawals for 158 months.

Step-by-step explanation:

To determine how long $570,000 will sustain month-end withdrawals of $3,800, we need to calculate the number of payments, n. We can use the formula for the future value of an annuity to solve for n:

570,000 = 3,800 * [(1 + 0.0425/12)^n - 1] / (0.0425/12)

After solving this equation, we find that n is approximately 157.4. Since we need to round up to the next whole number, n would be 158. Therefore, the money will sustain the withdrawals for 158 months.