# Annual Percantage & Fixed rate Problems

• Jan 26th 2007, 06:36 AM
fw_mathis
Annual Percantage & Fixed rate Problems
Can someone please get me on the right for setting up these problems? I guess I'm not grasping the concept of how to solve for the different periods of time. Please see attachment. If someone can just get me started by providing one example for one problem, I think I will be able to take it from there. Thanks to anyone who can help. :( :confused:
• Jan 26th 2007, 07:16 AM
Soroban
Hello, fw_mathis!

Quote:

I'm not grasping the concept of how to solve for the different periods of time.

Formula: . $A\;=\;P\left(1 + \frac{r}{n}\right)^{nt}$

. . $\begin{array}{ccccc}A: & \text{final amount} \\ P: & \text{principal invested} \\ r: & \text{annual interest rate} \\ n: & \text{number of periods per year} \\ t: & \text{number of years} \end{array}$

Quote:

1. Suppose you deposit \$20,000 for 3 years at a rate of 8%.
We have: . $P = 20,000,\;r = 0.08,\;t = 3$

Quote:

(a) Calculate the return $(A)$ if the bank compounds quarterly $(n = 4)$
We have: . $A \;=\;20,000\left(1 + \frac{0.08}{4}\right)^{4\cdot3} \;=\;25364.83589 \:\approx\:\25,364.84$

Quote:

(b) Calculate the return if the bank compounds monthly $(n = 12)$.
We have: . $A \;=\;20,000\left(1 + \frac{0.08}{12}\right)^{12\cdot3} \;=\;25404.74103\:\approx\:\25,404.74$

Quote:

(c) Calculate ther return if the bank compounds daily $(n=365)$.
We have: . $A \;=\;20,000\left(1 + \frac{0.08}{354}\right)^{365\cdot3} \;=\;25424.3144 \;\approx\;\25,424.31$

Quote:

(d) What observation can you make about the size of the increase in your return
as your compounding increases more frequently?

As the compounding becomes more frequent, the amount returned increases.

But the size of the increases is getting smaller.
. . From quarterly to monthly, the increase is: $\39.90$
. . From monthy to daily, the increase is: $\19.57$

Hope this helps . . .