A $1,600.00 principal earns 7% annual interest, compounded semiannually( twice per year). After 33 years, what is the balance in the account?
The formula to calculate the balance in an account with compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (balance)
P = the principal (initial amount) $1,600
r = the annual interest rate (7% or 0.07)
n = the number of times interest is compounded per year (2)
t = the number of years (33)
Let's plug in the values:
A = 1600(1 + 0.07/2)^(2*33)
Simplifying the exponent:
A = 1600(1.035)^(66)
A = 1600(3.604776175)
A ≈ $5,767.64
Therefore, after 33 years, the balance in the account will be approximately $5,767.64.