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Answer:
a)
[tex]A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}[/tex]
b)
The total amount accrued, principal plus interest, from compound interest on an original principal of $ 4,200.00 at a rate of 3.6% per year compounded 12 times per year over 10 years is $5667.28.
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\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}[/tex]
where
P represents the principal amount
r represents Annual Rate
n represents the number of compounding periods per unit t, at the end of each period
t represents the time Involve
b) What will the value be after 10 years?
Given
The principal amount P = $4200
Annual Rate r = 3.6% = 3.6/100 = 0.036
Compounded monthly = n = 12
Time Period = t
To Determine:
The total amount A = ?
Using the formula
[tex]A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}[/tex]
substituting the values
[tex]A\:=\:4200\left(1\:+\:\frac{0.003}{12}\right)^{\left(12\right)\left(10\right)}[/tex]
[tex]\:A\:=\:4200\left(1.0025\right)^{120}[/tex]
[tex]A=5667.28[/tex] $
Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 4,200.00 at a rate of 3.6% per year compounded 12 times per year over 10 years is $5667.28.