QuestionMay 30, 2025

(4) (10 points) Suppose you have 400,000 in a bank account when you retire, and you want that money to last for the next 15 years. How much money can you withdraw every week (assuming 52 weeks in a year ), if the bank offers an interest rate of 3.5% 7

(4) (10 points) Suppose you have 400,000 in a bank account when you retire, and you want that money to last for the next 15 years. How much money can you withdraw every week (assuming 52 weeks in a year ), if the bank offers an interest rate of 3.5% 7
(4) (10 points) Suppose you have 400,000 in a bank account when you retire, and you want
that money to last for the next 15 years. How much money can you withdraw every
week (assuming 52 weeks in a year ), if the bank offers an interest rate of 3.5%  7

Solution
4.2(184 votes)

Answer

\ 604.89 per week Explanation 1. Calculate the weekly interest rate Convert annual interest rate to weekly: r = \frac{0.035}{52}. 2. Determine total number of withdrawals Total weeks in 15 years: n = 15 \times 52. 3. Use annuity formula for withdrawal calculation Use the formula for annuity withdrawals: P = \frac{A \cdot r}{1 - (1 + r)^{-n}}, where A = 400,000. 4. Solve for weekly withdrawal amount Substitute values into the formula and solve for P.

Explanation

1. Calculate the weekly interest rate<br /> Convert annual interest rate to weekly: $r = \frac{0.035}{52}$.<br />2. Determine total number of withdrawals<br /> Total weeks in 15 years: $n = 15 \times 52$.<br />3. Use annuity formula for withdrawal calculation<br /> Use the formula for annuity withdrawals: $P = \frac{A \cdot r}{1 - (1 + r)^{-n}}$, where $A = 400,000$.<br />4. Solve for weekly withdrawal amount<br /> Substitute values into the formula and solve for $P$.
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