An initial deposit of $5000 earns 5.5% annual interest compounded semiannually. How much will be in the account after 5 years?
5000(1+ .055/2)^(2)(5)
To calculate the future value of the account after 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the account
P = the initial deposit
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the initial deposit (P) is $5000, the annual interest rate (r) is 5.5% or 0.055 as a decimal, the interest is compounded semiannually (n = 2), and the time (t) is 5 years.
Plugging in these values into the formula:
A = 5000(1 + 0.055/2)^(2 * 5)
Step 1: Simplify the interest rate per compounding period.
0.055/2 = 0.0275
Step 2: Calculate the exponent.
2 * 5 = 10
A = 5000(1 + 0.0275)^(10)
Step 3: Calculate the value inside the parentheses.
(1 + 0.0275) = 1.0275
A = 5000(1.0275)^(10)
Step 4: Raise the value inside the parentheses to the power of the exponent.
1.0275^10 ≈ 1.1618
A = 5000 * 1.1618
A ≈ $5809
Therefore, the amount in the account after 5 years will be approximately $5809.