Question

Problem 3: You are 62 years old today and can take your Social Security payments early or wait until your Full Retirement Age (FRA) of 67. If you start early, your monthly payments will be $1,700. If you wait until age 67, you'll receive monthly payments of $2,400. In either case your payments will start one month from the date at which you choose to start. If the discount rate is 2.8%, and you expect to live until age 84, what choice should you make. Assume no other factors apply to your decision. Hint, you must find the PV of both options AT age 62 to make a decision. 12 8 4 62 67 2.80% $2,400 $1,700 264 204 Number of monthly payments if taken early: Number of monthly payments if taken at FRA PV (at age 62) of payments if taken early: PV (at age 62) of payments if taken at FRA*: Choice: | Start at FRA

Answer 1

A B 1 Monthly payment at age of 62 Years $1,700.00 12 Time period in Months (82 Years - 62 Years) 264 =22*12 3 Prevailing market discount rate 2.80% 4 PV of monthly payment at age of 62 Years $334,787.16 =PV(B3/12,B2,-B1,0,0) 5 6 Monthly payment at age of 67 Years $2,400.00 17 Time period in Months (82 Years - 67 Years) 204 =17*12 8 Prevailing market discount rate 2.80% 19 PV of monthly payment at age of 67 Years $389,203.15 =PV(B8/12,B7,-B6,0,0) 10 PV of monthly payment at age of 62 Years $339,008.64 =B9/((1+B8)^5) 11 12 Since, PV of $2400 monthly payment at age of 67 Years is higher and hence chosen.