A $1,600.00 principal earns 7% annual interest, compounded semiannually (twice per year). After 33 years, what is the balance in the account?
(1 point)
Responses
$4,979.11
$14,920.54
$112,992.00
$15,494.70
To calculate the balance after 33 years with a $1,600 principal earning 7% annual interest compounded semiannually, you would use the formula:
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) = $1,600.00
r = the annual interest rate (decimal) = 7% = 0.07
n = the number of times that interest is compounded per year = 2
t = the number of years the money is invested or borrowed for = 33
Plugging in the 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(8.196021641)
A = $13,113.63
Therefore, the balance in the account after 33 years would be approximately $13,113.63.
None of the provided responses match this amount, so there may have been a mistake in calculation.