Question

carl puts 10,000 into a bank account that pays an annual effective interest rate of 4% for ten years. if a withdrawal is made during the first five and one-half years, a penalty of 5% of the withdrawal amount is made. carl withdraws k at the end of each of years 4, 5, 6 and 7. the balance in the account at the end of year 10 is 10,000. calculate k.

Answer 1

To determine the withdrawal amount 'k' that Carl can make and still have $10,000 remaining after ten years, given the interest and penalty conditions, we need to perform compound interest calculations accounting for the penalty on early withdrawals.

Step-by-step explanation:

Carl initially deposits $10,000 into a bank account with an effective annual interest rate of 4% for ten years. Withdrawals made within the first five and one-half years are subject to a 5% penalty. To solve for the withdrawal amount 'k' that Carl makes at the end of each of years 4, 5, 6, and 7 while maintaining a balance of $10,000 at the end of year 10, we have to use the formula for compound interest and incorporate the penalties for early withdrawal. To calculate k, we need to consider the compound interest Carl's account would accumulate over time without withdrawals and then account for the withdrawals, plus penalties when they are applied. This involves a bit of financial calculation and algebra.