Answer
$P \approx \$4,509.58$
Work Step by Step
RECALL:
The formula for the future value $A$ is:
$A=P(1+rt)$
where
P = principal amount borrowed
r = interest rate per year
t = time in years
Divide $(1+rt)$ on both sides of the formula given above to obtain:
$\dfrac{A}{1+rt}=P$
Thus, the principal or present value $P$ can be found using the formula above.
Use the formula above and the given values in the problem to obtain:
$P=\dfrac{\$5000}{1+14.5\% \cdot \frac{9}{12}}
\\P=\dfrac{\$5000}{1+0.145 \cdot 0.75}
\\P=\dfrac{\$5000}{1+.10875}
\\P=\dfrac{\$5000}{1.10875}
\\P=\$4,509.582864
\\P \approx \$4,509.58$
