626
FUTURE VALUE


You
just started your first job, and you want to buy a house within 3 years. You are currently saving for the down
payment. You plan to save $5,000 the
first year. You also anticipate that
the amount you save each year will rise by 10 percent a year as your salary
increases over time. Interest rates
are assumed to be 7 percent, and all savings occur at year end.
HOW
MUCH MONEY WILL YOU HAVE FOR A DOWN PAYMENT IN 3 YEARS?
627
REQUIRED ANNUITY PAYMENTS


A
15year security has a price of $340.4689.
The security pays $50 at the end of each of the next 5 years, and then
it pays a different fixed cash flow amount at the end of each of the
following 10 years. Interest rates are
9 percent.
WHAT
IS THE ANNUAL CASH FLOW AMOUNT BETWEEN YEARS 6 AND 15?

629
FUTURE VALUE OF AN ANNUITY


Erika
and Katherine have both been given $30,000 by their grandparents today on
their 25^{th} birthdays. They
want to save for their future and have aspirations of one day being
millionaires. Each woman plans to make
annual contributions on her birthday, beginning next year. Erika and Katherine have each opened
investment accounts at the First National Bank and Second National Bank,
respectively, and they expect to earn nominal returns of 8 and 9 percent,
respectively. Erika has already decided
to deposit $5,000 each year into her investment account, while Katherine is
unsure of the amount she will deposit annually.



(a.)

How
long will it take Erika before she reaches her investment goal of $1 million?



(b.)

If
Katherine decides to make the same annual contributions as Erika, how much
sooner would she reach the investment goal?

633
EXPECTED RATE OF RETURN


A
5year security has a price of $1,300.
The security pays $400 at the end of each of the next 5 years.
WHAT
IS THE EXPECTED RETURN OF THIS INVESTMENT TO THAT INVESTOR?
648
REQUIRED ANNUITY PAYMENTS


A
father is planning a savings program to put his daughter through
college. His daughter is now 13 years
old. She plans to enroll at the university
in 5 years, and it should take her 4 years to complete her education. Currently, the cost per year (for
everything—food, clothing, tuition, books, transportation, and so forth) is
$12,500, but a 5 percent annual inflation rate in these costs is forecasted. The daughter recently received $7,500 from
her grandfather’s estate; this money, which is invested in a bank account
paying 8 percent interest, compounded annually, will be used to help meet the
costs of the daughter’s education. The
remaining costs will be met by money the father will deposit in the savings
account. He will make 6 equal deposits
to the account, one deposit in each year from now until his daughter starts
college. These deposits will begin
today and will also earn 8 percent interest, compounded annually.



a.

What
will be the present value of the cost of 4 years of education at the time the
daughter becomes 18? [Hint: Calculate the future value of the cost (at
5%) for each year of her education, then discount 3 of these costs back (at
8%) to the year in which she turns 18, then sum the 4 costs.]



b.

What
will be the value of the $7,500 that the daughter received from her
grandfather’s estate when she starts college at age 18? [Hint:
Compound for 5 years at an 8 percent annual rate.]



c.

If
the father is planning to make the first of 6 deposits today, how large must
each deposit be for him to be able to put his daughter through college? [Hint:
An annuity due assumes interest is earned on all deposits; however,
the 6th deposit earns no interest—therefore, the deposits are an ordinary
annuity.]



Solution: finance data bank