Sample Problems—Time Value of Money
1.
Gomez Electronics needs to arrange financing for its expansion program.
Bank A offers to lend
Gomez the required funds on a loan where interest must be paid monthly, and the quoted annual rate is
8 percent.
Bank B will charge 9 percent, with interest due at the end of the year.
What is the
difference in the effective annual rates charges by the two banks?
2.
In 1889, Vincent Van Gogh’s painting, “Sunflowers”, sold for $125.
In 1987 it sold for $36 million.
Had the painting been purchased by your great-grandfather and passed on to you, how much would
your average annually compounded rate of return have been—n=98.
3.
You deposited $1,000 in a savings account that pays 8 percent interest, compounded quarterly,
planning to use it to finish your last year in college.
Eighteen months later, you decide to go the Rocky
Mountains to become a ski instructor rather than continue in school, so you close out your account.
How much money will you receive?
4.
Smokey Stack smokes a pack of cigarettes a day.
Each pack of cigarettes costs $2.25.
Smokey,
having learned about the time value of money in his finance class, is wondering how much money he
could accumulate if he quit smoking and invested the money.
Assuming, the
amount saved each year
is invested at the end of the year at a 8% rate of return, how much could Smokey accumulate during
the next 40 years (assume a 365-day year and that the cost of cigarettes stays constant over the 40 year
period)
5.
Your brother-in-law borrowed $1,000 from you 10 years ago and then disappeared.
Yesterday he
returned and expressed a desire to pay back the loan, including the interest that accrued since he
borrowed the money.
Assuming that you had agreed to charge him 7%, and assuming that he wishes
to make five equal annual payments beginning in one year, how much would your brother-in-law have
to pay you annually in order to extinguish the debt?
(Assume the loan continues to accrue interest at
7% per year.)
6.
You plan to deposit $2,500 annually into your retirement account.
You are trying to decide whether to
deposit the funds at the beginning of the year or at the end of the year.
How much more will you have
with beginning-of-the year deposits if you deposit to the account for the next 40 years and the
applicable interest rate is 10 percent?
7.
Drexel Corporation has been enjoying a phenomenal rate of growth since its inception one year ago.
Currently, its assets total $100,000.
If growth continues at the current annual rate of 12 percent,
compounded quarterly, what will total assets be in 2 ½ years?
8.
What is the effective annual percentage rate of 12 percent compounded monthly?
9.