First, we need to calculate the number of compounding periods. Since interest is compounded semiannually (twice a year), there will be 10 compounding periods in 5 years (5 years x 2 compounding periods per year).
Next, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount you will have after 5 years
P = the principal amount (the initial deposit)
r = the annual interest rate (6%)
n = the number of times the interest is compounded per year (2)
t = the number of years (5)
Plugging in the values, we get:
A = 900(1 + 0.06/2)^(2*5)
A = $1,178.16
Therefore, you would have $1,178.16 after 5 years if you deposit $900 and the interest rate is 6% compounded semiannually.
To calculate the amount you would earn with simple interest, we can use the simple interest formula:
I = Prt
Where:
I = the interest earned
P = the principal amount
r = the annual interest rate
t = the number of years
Plugging in the values, we get:
I = 900 * 0.06 * 5
I = $270
Therefore, you would earn $270 in interest after 5 years if you deposit $900 and the interest rate is 6% simple interest.