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Answer:
Step-by-step explanation:
a) How much will you have at the middle of the first year?
Using the formula
[tex]A\:=\:P\left(1+\frac{r}{n}\right)^{nt}[/tex]
where
Given:
Principle P = $300
Annual rate r = 6% = 0.06 per year
Compound n = Semi-Annually = 2
Time (t in years) = 0.5 years
To determine:
Total amount = A = ?
Using the formula
[tex]A\:=\:P\left(1+\frac{r}{n}\right)^{nt}[/tex]
substituting the values
[tex]A=300\left(1+\frac{0.06}{2}\right)^{\left(2\right)\left(0.5\right)}[/tex]
[tex]A=300\cdot \frac{2.06}{2}[/tex]
[tex]A=\frac{618}{2}[/tex]
[tex]A=309[/tex] $
Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 0.5 years is $ 309.00.
Part b) How much at the end of one year?
Using the formula
[tex]A\:=\:P\left(1+\frac{r}{n}\right)^{nt}[/tex]
where
Given:
Principle P = $300
Annual rate r = 6% = 0.06 per year
Compound n = Semi-Annually = 2
Time (t in years) = 1 years
To determine:
Total amount = A = ?
so using the formula
[tex]A\:=\:P\left(1+\frac{r}{n}\right)^{nt}[/tex]
so substituting the values
[tex]A\:=\:300\left(1+\frac{0.06}{2}\right)^{\left(2\right)\left(1\right)}[/tex]
[tex]A=300\cdot \frac{2.06^2}{2^2}[/tex]
[tex]A=318.27[/tex] $
Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 1 year is $ 318.27.