To calculate the final amount in an account with an initial investment of $14,000 at an 11% annual interest rate compounded semiannually for 4 years, use the compound interest formula. The final amount comes out to approximately $21,384.27.
To find the amount of money in an account after 4 years with an initial investment of $14,000 and an interest rate of 11% compounded semiannually, we can use the compound interest formula:
A = P(1 + r/n)nt
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
In this case:
P = $14,000
r = 0.11 (11% as a decimal)
n = 2 (since the interest is compounded semiannually)
t = 4 years
Now, we substitute our values into the formula and solve:
A = 14000(1 + 0.11/2)2⋅4
A = 14000(1 + 0.055)8
A = 14000(1.055)8
A is approximately $21,384.27
The money in the account at the end of the period is $21,384.27.