Question

1. Liz is retiring from the US Postal Service and will turn 70 next year. After 39 years of service, her monthly pension is $7,500. She does not qualify for Social Security. Liz has accumulated $700,000 in her thrift savings plan. The government requires that she convert it to an annuity or move it to a IRA. All of the money is pretax and tax can be avoided if it is moved to the IRA. The annuity will be calculated based on her life expectancy of 17.5 years after age 70. The current US Treasury long-term bond rate is 3 percent. How much will she get as an annuity monthly payment? Should Liz take the annuity or move the money to the IRA? The tax regulations require that she take out 4 percent of the amount each year.

2. Kathy plans to move to Maryland and take a job at McCormick as the assistant director of HR. She and her husband, Stan, plan to buy a house in Garrison, MD, and their budget is $500,000. They have $100,000 for the down payment and McCormick will pay for closing costs. They are considering either a 30-year mortgage at 4.5 percent annual rate or a 15 year mortgage at 4 percent. Calculate the monthly payment for each. Property taxes and insurance will add $1,000 per month to which ever mortgage they choose. What should Kathy and Stan do?

Answer 1

Monthly annuity can be calculated from following data,

PV = $700,000

NPER = 17.5 yr = 17.5*12 = 204 months

Rate = 3% = 3/12 = 0.25% monthly rate

PMT =? [ PMT(rate, NPER, -PV) : PMT(0.25%,204,-700000] = $ 4,384.62

Monthly annuity = $ 4,384.62

In case of mandatory withdrawal of 4% every so, withdrawal amount = $ 700,000 * 4% = $ 28,000

It is better to get annuity at this age of 70 years .

Answer 2)

Budgeted price = $ 500,000

Down payment = $ 100,000

Loan Amount(PV)= $ 500,000 - $ 100,000 = $ 400,000

Condition 1 , 4.5% , 30 years mortgage

rate = 4.5% = 4.5/12 = 0.375%

NPER = 30 years = 30* 12 = 360 months

Monthly installment : [PMT( 0.375% ,360, -400000)]

Monthly Installment : $ 2,026.74

Total Interest paid = $ 2,026.74 *360 - 400,000 = $ 329,626.4

Condition 2: 4% , 15 years mortgage

rate = 4% = 4/12 = 0.333%

NPER = 15 years = 15* 12 = 180 months

Monthly installment : [PMT( 0.333% ,180, -400000)]

Monthly Installment : $ 2,957.95

Total Interest paid = $ 2,957.95 *180 - 400,000 = $ 132,431

Here, net interest rate in condition 2 is much less than condition 1 , although monthly payment in condition 2 is higher than condition 1.

If they have money to pay higher monthly installment , condition 2 is better option.