Below are several problems that allow you to use
your knowledge and problem solving skills:
1) At
birth, your Uncle Hans secretly purchased a $5000 U.S. Savings Bond for
$2500. The conditions of the bond state
that the US Government will pay a minimum annual interest rate of r = 8.75%,
compounded quarterly. Your uncle has
given you the bond as a gift, subject to the condition that you cash the bond
at age 35 and buy a red Porsche. On
your way to the dealer, you receive a call from you tax accountant informing
you of a 28% tax on capital gains you realize through cashing in the bond; the
capital gain is the selling price of the bond minus the purchase price. Before stepping into the showroom, compute
how much cash will you have on hand, after the US Government shares in your
profits.
2) Aunt
Bertha problems:
a) She
invested $2500 at 9.875% interest compounded continuously when you were 5 yrs
old for your college education. You are
now 18 yrs old. How much do you have
for your education?
b) You
are now 24 yrs old and you found out that she bought a US savings bond for
$1200 when you were 2 yrs old which was compounded continuously. It is now worth $32,785.12. What was the rate of interest?
c) You
are now 32 years old and you want to buy a house. Your aunt has invested some money when your where 18 yrs
old. You checked with the bank and they
told you that the interest rate was 8.75% compounded continuously and the
account is worth $102,834.25. How much
did she originally invest?
3) If $2,000 is invested in a continuously
compounding savings account and we want the value after 12 years to be 130,000,
what is the required annual interest rate?
If instead, the same $2,000 is invested in a continuously compounding
savings account with r = 6.4% annual interest, when will the exact account
value be $130,000?
4)The earning power of men and women in the
business work force can be modeled by
exponential equations. The
equation for the men's earning power is y = 9521(1.0662066)x and the
women's equation y = 5616(1.0727495)x. Determine when the earning power of the women will exceed the
men's.