PART 1: INTRODUCTION
ADDITIONAL APPLICATIONS INVOLVING LUMP SUMS
P3-4 You have saved $10,000 toward a down payment on a home. The money is invested in an account earning
7% interest. You will be ready to purchase the new home once your savings account grows to $25,000.
a Approximately how many years will it take for the account to reach $25,000?
b If the interest rate doubles to 14%, how many years will pass before you reach your $25,000
target?
P3-5 Find the rates of return required to do the following:
a Double an investment in four years
b Double an investment in 10 yearsc Triple an investment in four years
d Triple an investment in 10 years.
P3-6 The viatical industry offers a rather grim example of present-value concepts. The structure began in
the US in 1989. A company in this business, called a viator, purchases the rights to the benefits from
a life insurance contract from a terminally ill client. The viator may then sell claims on the insurance
payout to other investors. The industry began in the early 1990s as a way to help HIV/AIDS patients
capture some of the proceeds from their life-insurance policies for living expenses. A variant of this,
called accelerated death benefits, was created by insurance companies themselves, first in South
Africa, spreading on to Australia and then to the US. Under this model, the insurance company itself
pays a large portion of the death benefits to the patient before their death in order to help them
cover the costs of supporting their life-threatening illness, such as HIV/AIDS or cancer. This model
tends to be most effective for those terminally ill people with few dependants who will survive them.
Suppose a patient has a life expectancy of 18 months and a life-insurance policy with a death
benefit of $100,000. A viator pays $80,000 for the right to the benefit and then sells that claim to
another investor for $80,500.
a From the point of view of the patient, this contract is like taking out a loan. What is the compound
annual interest rate on the loan if the patient lives exactly 18 months? What if the patient lives
36 months?
b From the point of view of the investor, this transaction is like lending money. What is the compound
annual interest rate earned on the loan if the patient lives 18 months? What if the patient lives just
12 months?FUTURE VALUE OF CASH FLOW STREAMSP3-7 Liliana Alvarez’s employer offers its workers a two-month paid sabbatical every seven years. Liliana,
who just started working for the company, plans to spend her sabbatical touring Europe at an
estimated cost of $25,000. To finance her trip, Liliana plans to make six annual end-of-year deposits
of $2,500 each, starting this year, into an investment account earning 8% interest.
a Will Liliana’s account balance at the end of seven years be enough to pay for her trip?
b Suppose Liliana increases her annual contribution to $3,150. How large will her account balance
be at the end of seven years?P3-8 Robert Williams is considering an offer to sell his medical practice, allowing him to retire five years
early. He has been offered $500,000 for his practice and can invest this amount in an account
earning 10% per year. If the practice is expected to generate the cash flows listed below, should
Robert accept this offer and retire now?End of year Cash flow
1 $150,000
2 150,000
3 125,000
4 125,000
5 100,000