Answer
The amount owed at the end of 5 years is $\$2509.30$.
Work Step by Step
RECALL:
The future value $A$ of an investment/loan that is compounded continuously is given by the formula:
$A=Pe^{rt}$
where
$P$ = amount invested/borrowed
$r$ = annual interest rate
$t$ = time in years
The given problem has:
$P =\$1600 $
$r=9\%=0.09$
$t=5$ years
Substitute the values into the given formula above to obtain:
$A=\$1600(e^{0.09(5)})
\\A=\$2509.299497
\\A\approx \$2509.30$
Thus, the amount owed at the end of 5 years is $\$2509.30$.
