The correct answer is $15,494.70.
To calculate the future value of the principal, we can use the formula for compound interest:
\[A = P \left(1 + \frac{r}{n}\right)^{nt}\]
Where:
A = future value of the principal
P = initial principal
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Plugging in the given values:
P = $1600
r = 7% = 0.07
n = 2 (compounded semiannually)
t = 33
\[A = 1600 \left(1 + \frac{0.07}{2}\right)^{2 \cdot 33}\]
\[A = 1600 \left(1 + 0.035\right)^{66}\]
\[A = 1600 \cdot 1.035^{66}\]
\[A = 1600 \cdot 8.820271\]
\[A = 14,112.4336\]
Therefore, after 33 years, the principal will grow to $14,112.43. However, this answer is not one of the options provided.
It seems that there might be an error in the answer choices, as none of them match the calculated future value.
$1600 principal earning 7%, compounded semi annually, after 33 years.
$4979.11
$14,920.54
$112,992.00
$15,494.70
1 answer