Question 192945
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Step 1 is to write your formula correctly.  You left out a very important parenthesis mark.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A = P\left(1 + \left(\frac{r}{n}\right)\right)^{nt}]


<i>A</i> is the answer you want.


<i>P</i> is the amount invested, or $40,600


<i>r</i> is the annual interest rate, expressed as a decimal, so 0.10


<i>t</i> is the number of years, or 5 for this problem


and <i>n</i> is the number of compounding periods per year, so


For Annually:  <b><i>n</i> = 1</b>


For Semi-annually:  <b><i>n</i> = 2</b>


For Monthly:  <b><i>n</i> = 12</b>


For Daily: <b><i>n</i> = 365</b>


Just substitute the values for the variables in the formula and get to punching buttons on your calculator.


For example, for the Monthly problem:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A = 40600\left(1 + \left(\frac{0.10}{12}\right)\right)^{(12\cdot5)} = 66799.54]


However, for Continuous, you have to use a different formula.  That's because *[tex \large n = \infty] for continuous compounding.  As it turns out,


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \lim_{n\rightarrow\infty}\left(1 + \left(\frac{r}{n}\right)\right)^{nt} = e^{rt}]


So, for continuous compounding:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A = Pe^{rt}]


Where <i>e</i> is the base of the natural logarithms.  Again, substitute and punch calculator buttons.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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