Question

Bill Petty,56 just retired after 31 years of teaching. He is a husband and father of two children who are still dependent. He received a $150000 lump-sum retirement bonus and will receive $2800 per month from his retirement annuity. He has saved $150000 in a 403(b) retirement plan and another $100000 in other accounts. His 403(b) plan is invested in mutual funds, but most of his other investments are in bank accounts earning 2 or 3 percent annually. Bill has asked your advice in deciding where to invest his lump-sum bonus and other accounts now that he has retired. He also wants to know how much he can withdraw per month, considering he has two children and a nonworking spouse. Because he has children, his current monthly expenses total $5800. He is not eligible for Social Security until age 62, when he will draw approximately $1200 per month, however, he would rather defer drawing on Social Security until age 67 to increase his monthly benefit amount of $1550.

A) Bill has an emergency fund already set aside, so he can use his $400000 of savings for retirement. How much can he withdraw on a monthly basis to supplement his retirement annuity if his investments return 5% annually and expects to live 30 more years?

B) Ignoring his Social Security benefit , is the amount determined in Question 1 sufficient to meet his current monthly expenses (keep in mind he will receive a pension of $2800 per month)? If not, how long will his retirement last if his current expenses remain the same?

What if his expenses are reduced to $4,500 per month?

C) Considering the information obtained in question 2, should Bill wait until age 67 for his Social Security benefits? If he waits until age 67, how will his Social Security benefits change the answer to question 2?

D) If the inflation rate average 3.5% during Bill’s retirement, how old will he be when prices have doubled from current levels? How much will a soda cost when Bill dies, if he lives the full 30 years and the soda costs $1 today?

Answer 1

Question A.

The $400,000 will give monthly payment of $2,147.29 for 30 years as follows:

Question B

Current monthly pension= $2,800

Monthly Annuity as per part A above= $2,147.29

Total amount available monthly: $2,800+ $2,147.29 = $4,947.29

Current monthly expenses is given as $5,800. Hence the amount as above is not sufficient.

Reducing the current pension of $2,800, annuity required every month to support the current expenses= $5,800-$2,800= $3,000

This amount will be available for about 195.03 months, ascertained using the NPER function of Excel as follows:

In case the expenses are reduced to $4,500 per month, net annuity required= $4,500- $2,800 = $1,700

This amount will be available for 945.60 months as follows:

Question C

It is assumed that the the 'question 2' referred to is question B.

If the monthly expenses are retained at $5,800 the annuity of $3,000 will be available for about 195/12= 16.25 years ie., till the age of 72. On the other hand, if the expenses are at $4,500 per month, it is sufficient for 945/12= 78.75 months. Hence it is better to wait till age 67 for social security benefits and get the enhanced amount of $1,550 per month.

Question D

Doubling period = ln2/ ln(1+r) Where ln2= natural logarithm of 2 which is 0.693147

                                ln(1+r) = natural logarithm of exponent of growth ie., (1+r)

Given, rate of growth (inflation)= 3.5%,

Hence, Doubling period= 0.693147/In(1.035) = 0.693147/0.034401426= 20.148788686 years.

Bill will be 56+20.15= more than 76 years by then.

Given, Cost of Soda now= $1. Inflation rate=3.5%

Cost of soda after 30 years= (1+3.5%)^30 = 1.035^30 =$2.806794