Page 291 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

14. Using what you know about the time value of money, calculate the error in using the above equation
to estimate how long it takes to double an investment made at the following effective annual interest
rates: 5%, 7.5%, and 10%.

Express your answers as % error to two significant figures.

Comment on the Rule of 72 and its accuracy for typical financial calculations today.

You invested $5000 eight years ago, and you want to determine the value of the investment now, at
the end of year 8. During the past eight years, the nominal interest rate has fluctuated as follows.

15.

If your investment is compounded daily, how much is it worth today? (Ignore the effect of leap years.)

What are the differences between investing $15,000 at 9% p.a. for 15 years when compounded
16.
yearly, quarterly, monthly, daily, and continuously? Ignore the effect of leap years.

One bank advertises an interest rate on a certificate of deposit (CD) to be 4% compounded daily.
17.
Another bank advertises a CD with a 4.1% effective annual rate. In which CD would you invest?

You want to begin an investment plan to save for your daughter’s college education. Because you
believe that your newly born daughter will be a genius (just like you!), you are assuming the cost of

an Ivy League education. You plan to put money into an investment account, at the end of each year,
for the next 18 years. You believe that you will need about $75,000 per year, each year, 19 through
18. 22 years from now.
a. Draw a discrete cash flow diagram for this situation.
b. How much would you have to invest each year to pay for college and have a zero balance at
the end of year 21? The effective annual interest rate of your investment is 8%.
c. What interest rate would be needed if you could invest only $5000/yr?

You begin an investment plan by putting $10,000 in an account that you assume will earn 8%
annually. For the next 25 years, you add $5000 per year. In anticipation of buying a house with a 15-
year mortgage, you expect to need a one-time down payment of $55,000 at the end of year 8. You

anticipate being able to make the monthly mortgage payment without affecting the yearly contribution
19.
to the savings plan.
a. Draw a discrete, nondiscounted cash flow diagram for this situation.
b. Will you have the down payment at the end of year 8?