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# Time Value Money for Retirement Planning

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63. Retirement Planning. A couple will retire in 50 years; they plan to spend about \$30,000 a
year in retirement, which should last about 25 years. They believe that they can earn 10 percent
interest on retirement savings.
a. If they make annual payments into a savings plan, how much will they need to save each
year? Assume the first payment comes in 1 year.
b. How would the answer to part (a) change if the couple also realize that in 20 years, they
will need to spend \$60,000 on their child's college education?

74. Retirement and Inflation. Redo part (a) of problem 63, but now assume that the inflation rate over the next 50 years will average 4 percent.

a. What is the real annual savings the couple must set aside?
b. How much do they need to save in nominal terms in the first year?
c. How much do they need to save in nominal terms in the last year?
d. What will be their nominal expenditures in the first year of retirement? The last?

#### Solution Summary

The solution examines the time value of money for retirement planning.

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## Time value of money: retirement plans

Ted Gardiner has just turned 30 years old. He has currently accumulated \$35,000 toward his planned retirement at age 60. He wants to accumulate enough money over the next 30 years to provide for a 20-year retirement annuity of \$100,000 at the beginning of each year, starting with his 60th birthday. He plans to save \$5,000 at the end of each of the next 10 years. What equal amount must he save at the end of years 11 through 30 to meet this objective? The interest rate for the first 10 years will be 5 percent. After that time, the interest rate is expected to be 7 percent.

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