what is the total investment after 2 years if 400$ at 9% is compounded semi-annually for 2 years
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I= (400)(0.09)(2)
I= 72
To calculate the total investment after 2 years with compounded interest, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount after time t
P = the principal amount (initial investment)
r = the annual interest rate (written as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $400, the annual interest rate (r) is 9% (which is equivalent to 0.09 as a decimal), the number of times interest is compounded per year (n) is 2 (since it is compounded semi-annually), and the number of years (t) is 2.
Using the formula, we can calculate the total investment:
A = 400(1 + 0.09/2)^(2*2)
A = 400(1 + 0.045)^4
A = 400(1.045)^4
Simplifying further:
A = 400(1.193416801)
A ≈ 477.3667204
Therefore, the total investment after 2 years with $400 at 9% compounded semi-annually would be approximately $477.37.