Answer:
To calculate the rate on the retirement account needed for Derek to have $3,420,825.00 when he retires, we can use the formula for compound interest: A = P(1 + r/n)^(nt) Where: A is the future value of the account P is the principal amount (initial deposit) r is the annual interest rate (in decimal form) n is the number of times interest is compounded per year t is the number of years In this case, Derek is making deposits on each birthday from his 27.00th to his 69.00th, so there are 69 - 27 + 1 = 43 deposits. Let's assume the rate is compounded annually (n = 1). Since the amount of each deposit is $11,163.00, the principal amount (P) is 43 * $11,163.00 = $480,909.00. We want to find the interest rate (r) that will give us a future value (A) of $3,420,825.00 when Derek retires. Rearranging the formula, we have: r = (A/P)^(1/(nt)) - 1 Substituting the given values, we have: r = ($3,420,825.00/$480,909.00)^(1/(43*1)) - 1 Simplifying the calculation, we find that the rate on the retirement account will need to be approximately 0.0627 or 6.27% for Derek to have $3,420,825.00 when he retires.