A $1,600.00 principal earns 7% annual interest, compounded semiannually (twice per year). After 33 years, what is the balance in the account?
To calculate the balance in the account after 33 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
In this case:
P = $1,600.00
r = 7% or 0.07
n = 2 (interest is compounded semiannually)
t = 33 years
Plugging in these values:
A = $1,600(1 + 0.07/2)^(2*33)
A = $1,600(1 + 0.035)^66
A = $1,600(1.035)^66
A = $1,600(4.004119)
A = $6,406.59
So, the balance in the account after 33 years will be $6,406.59.