Find the amount owed at the end of 4 years if $3,000 is borrowed at a rate of 7% compounded semiannually (twice a year).(1 point)
Responses
$3,442.57
$3,442.57
$5,154.56
$5,154.56
$3,932.39
$3,932.39
$3,950.43
To find the amount owed at the end of 4 years, we need to calculate the future value of the loan.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the loan
P = the principal amount (initial loan amount) = $3,000
r = annual interest rate (7%) = 0.07
n = number of times the interest is compounded per year = 2 (semiannually)
t = number of years = 4
Plugging in the values into the formula:
A = 3000(1 + 0.07/2)^(2*4)
A = 3000(1 + 0.035)^8
A = 3000(1.035)^8
A ≈ $3,932.39
Therefore, the amount owed at the end of 4 years is approximately $3,932.39.