Question

Your grandparents are asking you for advice on when they should start collecting social security payments. If they wait until age 66, they will collect $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

A.

With lower payments starting at the age of 62, annual payment = 1500*12 = $18000

With higher payments starting at the age of 66, annual payment = 2000*12 = $24000

Before the higher payment starts, the amount of lower payment already paid = time*lower annual payments

Before the higher payment starts, the amount of lower payment already paid = 4*18000 = $72000

So,

Time taken by the higher dollar payment to catch up = 72000/(24000-18000)

Time taken by the higher dollar payment to catch up = 12 years

Hence,

If lower dollar payment starts in 62 years and higher dollar payment starts in 66 years, then it is by the 78 years (66 year + 12) , when higher dollar catch up the lower dollar payment.

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B.

R = 6%

With lower payment, time = 23 years

So

PW of the lower payment = 18000*(1-1/(1+6%)^23)/.06

PW of the lower payment = $221460.8 or $221461

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With higher payment, time = 19 years

So

PW of the higher payment = 24000*(1-1/(1+6%)^19)/.06

PW of the higher payment = $267794.8 or $267795