Final answer:
Dan needs to invest approximately $1,063,830 in the CD, which when rounded to the nearest thousand is $1,064,000, to have a yearly income of $50,000 from a CD with 4.7% APR compounded annually.
Step-by-step explanation:
The student asked how much money Dan needs to invest in a CD with a 4.7% APR, compounded annually, in order to have a yearly income of $50,000 upon retirement. To solve this, we use the formula for the future value of an investment under compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time in years.
Since the interest is compounded annually, n would be 1. However, we actually need to rearrange the formula to solve for the principal P, since we are given A (the desired yearly income of $50,000) and we want to find out how much needs to be initially invested. In this case, we will use the formula P = A / (1 + r)^t. Since t is not provided, we will assume Dan wants to withdraw this amount perpetually, focusing only on the interest generated per year (interest rate multiplied by the principal).
Therefore, the investment Dan needs is P = $50,000 / 0.047. After calculating, we find that Dan would need to invest approximately $1,063,830, which, when rounded to the nearest thousand dollars, gives us option (d) $1,064,000.