Rebecca is retiring next month when she turns 65.She can select a pension of $1745 monthly guaranteed for the rest of her life,but not indexed for inflation,or take a lump sum of $312 000.Assume she can invest the lump sum at five percent annually and draw the same income as the pension.What age must she reach for the monthly pension to be the better choice?
A)89
B)90
C)92
D)93

Question

Quizplus · Accepted Answer

First, we need to calculate how much income Rebecca can generate from the lump sum of $312,000 at a rate of 5%. The annual income from this lump sum would be $15,600 ($312,000 x 0.05). Monthly income would be $1300 ($15,600/12).

Now, we need to calculate how much income Rebecca would receive from the pension if she lives for a certain number of years. Let's assume that she lives to the age of n years. The total income she would receive from the pension over these n years would be $1745 x 12 x n = $20,940n.

The total income she would receive from the lump sum over the same n years would be $1300 x 12 x n = $15,600n.

Therefore, the pension would be a better choice if:

$20,940n > $15,600n

n > 3.25

This means that Rebecca would need to live for more than 3.25 years, or about 39 months, for the pension to be a better choice.

Assuming she retires at 65, she would need to reach the age of 92 (65 + 27) for the pension to be a better choice. Therefore, the answer is C) 92.

Rebecca Is Retiring Next Month When She Turns 65