Rebecca is retiring next month when she turns 65.She can select a pension that pays $1745 at the end of every month 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

To compare the two options, we need to find the present value of the monthly pension payments. We can use the present value formula for an ordinary annuity to do this:

PV = PMT * ((1 - (1 + r)^(-n)) / r)

Where PV = present value, PMT = monthly payment, r = annual interest rate (0.05/12), and n = number of payments.

Using the given numbers, we get:

PV = 1745 * ((1 - (1 + 0.05/12)^(-12*20)) / (0.05/12)) ≈ $286,318

So the lump sum option is better if it is greater than $286,318. Since it is $312,000, Rebecca should take the lump sum.

To figure out when the monthly pension would become the better option, we need to find how long it would take for the present value of the pension payments to exceed $312,000. We can use the same formula as above, but solve for n instead:

n = -log(1 - (PV*r)/PMT) / (12*log(1+r))

Plugging in the given numbers and solving for n, we get:

n ≈ 27.5 years

So Rebecca would need to live to age 65 + 27.5 = 92.5, or rounded up to age 93, for the monthly pension to be the better choice.

Rebecca Is Retiring Next Month When She Turns 65