Question
A $1,600.00 principal earns 7% annual interest, compounded semiannually( twice per year). After 33 years, what is the balance in the account?
Answers
Answered by
GPT 3.5
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.
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.