Answer:
Part 1) 
Part 2) 
Part 3) 
Part 4) 
Part 5) The Option A is the best way to invest the money by $4,223.94 than Option B
Step-by-step explanation:
Part 1)
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
Part 2)
we know that
The formula to calculate continuously compounded interest is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
substitute in the formula above
Part 3)
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
![P=40,000/[(\frac{12.0475}{12})^{216}]](https://tex.z-dn.net/?f=P%3D40%2C000%2F%5B%28%5Cfrac%7B12.0475%7D%7B12%7D%29%5E%7B216%7D%5D)
Part 4)
we know that
The formula to calculate continuously compounded interest is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
substitute in the formula above
Part 5)
<u><em>Option A</em></u>
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
<u><em>Option B</em></u>
we know that
The formula to calculate continuously compounded interest is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
substitute in the formula above
Compare the options
Option A ------> 
Option B -----> 
so
Option A > Option B
Find out the difference
therefore
The Option A is the best way to invest the money by $4,223.94 than Option B
