Question 192945: I am having problems with this particular word problem, I know I use the formula : A = P (1+(r/n)^nt but I am not sure how to use it in correlation to the problem, could someone help?
Problem :
If 40600 dollars is invested at an interest rate of 10 percent per year, find the value of the investment at the end of 5 years for the following compounding methods.
Annually : ?
Semi-annually : ?
Monthly : ?
Daily : ?
Continously : ?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Step 1 is to write your formula correctly. You left out a very important parenthesis mark.
\right)^{nt})
A is the answer you want.
P is the amount invested, or $40,600
r is the annual interest rate, expressed as a decimal, so 0.10
t is the number of years, or 5 for this problem
and n is the number of compounding periods per year, so
For Annually: n = 1
For Semi-annually: n = 2
For Monthly: n = 12
For Daily: n = 365
Just substitute the values for the variables in the formula and get to punching buttons on your calculator.
For example, for the Monthly problem:
\right)^{(12\cdot5)} = 66799.54)
However, for Continuous, you have to use a different formula. That's because  for continuous compounding. As it turns out,
\right)^{nt} = e^{rt})
So, for continuous compounding:
Where e is the base of the natural logarithms. Again, substitute and punch calculator buttons.
John
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