Question

Your grandparents are asking you for advice on when they should start collecting social secuni payments. If they wait until age 66, they will col- lect $2000 per month; but if they start collecting at age 62, they will collect $1500 per month. Assume they live to be 85, and simplify by assuming annual payments.

(a) When do the higher payments catch up in total dollars received with the lower payment that starts earlier?
(b) If their interest rate is 6%, which plan has a higher PW?

Answer 1

Answer:

a) Let the catchup takes place at the age of X years from the time when they are 62 years of age. Then their accumulated benefits will be

(X - 62)*1500 = (X - 66)*2000

1500X - 93000 = 2000X - 132000

500X = 39000

This gives X = 78. Hence at the end of 77 years or in the beginning of 78 years of age, the accumulated benefits will be equal independent of when they start

b) When the interest rate is 6%, PW is given by

PW(early starters) = 1500*(P/A, 6%, (85 - 62)) PW(late starters) = 2000*(P/A, 6%, (85 - 66))

= 1500*12.3034 = 18455.1 = 2000*11.1581 = 22.316.2

Hence, present worth of second plan of strating late has a higher PW.

Explanation: