5670 is invested at a anual intrest rate 3.5% for one year. if the intrest is compounded semiannually then the polynomial P(1+r/2)^2 represent the value of the investment after one year
Substitute 5670 for P.
and .035 for r.
add 1 to .035/2
Square that answer and then multipl by 5670
To find the value of the investment after one year when the interest is compounded semiannually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value of the investment
P is the principal or initial amount invested
r is the annual interest rate
n is the number of times the interest is compounded per year
t is the number of years
In this case:
P = $5670
r = 3.5% = 0.035
n = 2 (compounded semiannually)
t = 1 year
Plugging in the values into the formula, we get:
A = 5670(1 + 0.035/2)^(2*1)
Simplifying further:
A = 5670(1 + 0.0175)^2
Now, let's evaluate this expression to find the value of the investment after one year:
A = 5670(1.0175)^2
A = 5670(1.03505625)
A ≈ $5866.44
So, the value of the investment after one year, when the interest is compounded semiannually, is approximately $5866.44.
Therefore, the polynomial P(1+r/2)^2 = 5670(1 + 0.035/2)^2 represents the value of the investment after one year when the interest is compounded semiannually.