Respuesta :
Answer:
The amount in the account is $3062.4 (Approx) and compound interest is $162.4 .
Step-by-step explanation:
Formula for compounded semiannually
[tex]Amount = P(1 + \frac{r}{2} )^{2t}[/tex]
Where P is the principle , r is the rate in decimal form and t is the time.
As given
Michael arthur deported $2,900 in a new regular savings account that earns 5.5 percent interest .
Here
Principle = $2,900
5.5% is written in the decimal form.
[tex]= \frac{5.5}{100}[/tex]
= 0.055
Time = 1 year
Put in the formula
[tex]Amount = 2900\times (1 + \frac{0.055}{2} )^{2\times 1}[/tex]
[tex]Amount = 2900\times (1 + 0.0275 )^{2\times 1}[/tex]
[tex]Amount = 2900\times (1.0275)^{2}[/tex]
[tex]Amount = 2900\times 1.056\ (Approx)[/tex]
Amount = $ 3062.4 (Approx)
Thus the amount after 1 years is $3062.4 (Approx) .
Now find out the compound interest .
Amount = Principle + Compound interest
Here
Amount = $ 3062.4
Principle = $2,900
Put in the above
$3062.4 = $2,900 + Compound interest
Compound interest = $3062.4 - $2,900
Compound interest = $162.4
