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Answer:
a)
The function that represents the value of the account at any time, t
[tex]\:\:A=Pe^{rt}[/tex]
b)
The total amount accrued, principal plus interest, from compound interest on an original principal of $ 5,500.00 at a rate of 3.75% per year compounded continuously over 6 years is $ 6,887.77.
Step-by-step explanation:
a. Write the function that represents the value of the account at any time, t.
The function that represents the value of the account at any time, t
[tex]\:\:A=Pe^{rt}[/tex]
where
A represents the Future Value
P represents the Principle (Initial Value)
r represents the Interest rate
t represents the time
b) What will the value be after 6 years?
Given
The principal amount P = $5500
Annual Rate r = 3.75% = 3.75/100 = 0.0375
Time Period t = 6 years
To Determine:
The total amount A = ?
Using the formula
[tex]\:\:A=Pe^{rt}[/tex]
substituting the values
[tex]A\:=\:5500\left(2.71828\right)^{\left(0.0375\right)\left(6\right)}[/tex]
[tex]A=5500\cdot \:2.71828^{0.225}[/tex]
[tex]A = $ 6,887.77[/tex] $
Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 5,500.00 at a rate of 3.75% per year compounded continuously over 6 years is $ 6,887.77.