im doing corespondence and i tried for days to figure this out and i cant can anyone help??
Determine the amount of each investment? $400 at 9% compounded semi-annually for 2 years i just need that answer and how too get it then i can do them thank you
All calculations are based on the assumption that $400 is the initial
investment. If that is not true,let
me know and I'll redo the cal. based
on the new INFO.
Pt = Po * (r + 1)^n
r = ((9 / 12)/ 100) * 6 = 0.045 = Semi-
annual rate expressed as a decimal
n = 2 yr. / 0.5 = 4 = The number of
compounding periods.
Pt = 400 * (0.045)^4 = 477.01 = The
value of the investment after 2 yrs.
i don't understand still please help with showing how you got that answer thank you
To determine the amount of each investment, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (including principal and interest)
P = Principal amount (initial investment)
r = Annual interest rate (expressed as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, the principal amount (P) is $400, the annual interest rate (r) is 9% (0.09 as a decimal), the interest is compounded semi-annually (n = 2), and the investment period is 2 years (t = 2).
Plugging in the values into the formula, we get:
A = 400(1 + 0.09/2)^(2*2)
Simplifying the equation:
A = 400(1 + 0.045)^4
A = 400(1.045)^4
Calculating (1.045)^4:
A = 400(1.1851)
A = 474.04
Therefore, the amount of the investment, including principal and interest, after 2 years will be $474.04.
To calculate this, you can use a scientific calculator or a spreadsheet program like Microsoft Excel by entering the formula and substituting the appropriate values.