# Growth Periods - Continuous Growth

• May 1st 2006, 07:04 AM
shirel
Growth Periods - Continuous Growth
I have to work on these questions and write the answers down in an essay. Who can help me?? :)

In this project you will compare saving plans. For instance, you deposit \$1000 in a savings account and the following options are given:

a. 6.2% annual interest rate, compounded annually
b. 6.1% annual interest rate, compounded quarterly
c. 6.0% annual interest rate, compounded continuously

1) For each option, write a function that gives the balance as a function of the time t (in years).

2) Find the balance for the three options after 25, 50, 75 and 100 years. Is the option that yields the greatest balance after 25 years the same option that yields the greatest balances after 50, 75, 100 years? Explain!

3) Use a graphing utility to graph all three functions in the same viewing window. Can you find a viewing window that distinguishes among the graphs of the three functions? If so, describe the viewing window.

4) The effective yield of a savings plan is the percent increase in the balance after 1 year. Find the effective yields for three options listed above. How can the effective yield be used to decide which option is best?
• May 1st 2006, 02:25 PM
ThePerfectHacker
The formula is,
$P(t)=P_0(1+r/n)^{nt}$
Where P_0 is initial money,
r is rate of interest,
n is number of times a year,
t is number of years.

When you compound something countinously, the formula is,
$P(t)=P_0e^{rt}$
----------------------------
(1)
$P(t)=1000(1.062)^t$-------Anally
$P(t)=1000(1.01525)^{4t}$------Quaterly
$P(t)=1000e^{.06t}$------Countinously
• May 1st 2006, 03:19 PM
ThePerfectHacker
Quote:

Originally Posted by shirel
3) Use a graphing utility to graph all three functions in the same viewing window. Can you find a viewing window that distinguishes among the graphs of the three functions? If so, describe the viewing window.

Good luck with that. The problem is all these 3 graphs are so close that it is barely distinguishable. On the TI-89 there is no way you can distinguish.
The interval I used was
$0\leq x\leq .001$
$999.99\leq y\leq 1000.01$

This also answers the next question, the best one is the second one, then the first one then the last one.