Assume that you are 40 years old and wish to retire at age 65. You expect to be able to
average a 6% annual rate of interest on your savings over your lifetime (both prior to
retirement and after retirement). You would like to save enough money to provide
$8,000 per year beginning at age 66 in retirement income to supplement other sources
(social security, pension plans, etc.). Suppose you decide that the extra income needs to
be provided for only 15 years (up to age 80). Assume that your first contribution to the
savings plan will take place one year from now.
a. How much must you save each year between now and retirement to achieve your
goal?
Analyze the “expert’s” responses to the following questions:
Question: How early do you recommend people begin saving for retirement? Would it
be too early for my 14-year-old to start saving?
Expert: It’s never too early.
Question: For a college student, what would you suggest for a savings plan?
Expert: I’d suggest deciding on a specific amount to set aside each month, then
making sure you do it, no matter the temptations not to.
Fred’s company has a defined-benefit pension plan. Suppose the plan pays a benefit equal to 1% of final salary per year of service. Fred is 40 years old and has worked for the company for 15 years. His last year’s salary was $50,000 and is expected to remain so in real terms until retirement. The expected rate of inflation is 4%.
a. If normal retirement age is 65, the interest rate is 8%, and Fred’s life expectancy is 80, what is the present value of his accrued pension benefit?
Your great-aunt left you $20,000 when she died. You can invest the money to earn
12% per year. If you spend $3,540 per year out of this inheritance, how long will the
money last?
You win a $1 million lottery, which pays you $50,000 per year for 20 years. How
much is your prize really worth, assuming an interest rate of 8% per year?
In 1626 Peter Minuit purchased Manhattan Island from the Native Americans for
about $24 worth of trinkets. If the tribe had taken cash instead and invested it to earn
8% per year compounded annually, how much would the Indians have had in 1986,
360 years later?
You take a one-year installment loan of $1,000 at an interest rate of 12% per year (1%
per month) to be repaid in 12 equal monthly payments.
a. What is the monthly payment?
b. What is the total amount of interest paid over the 12-month term of the loan?
You want to establish a “wasting” fund, which will provide you with $1,000 per year
for four years, at which time the fund will be exhausted. How much must you put in the
fund now if you can earn 10% interest per year?
If you invest $100 every year for the next 20 years starting one year from today and
you earn interest of 10% per year, how much will you have at the end of the 20 years?
b. How much must you invest each year if you want to have $50,000 at the end of the
20 years?
If you invest $1,000 today at an interest rate of 10% per year, how much will you have
20 years from now, assuming no withdrawals in the interim?
