To solve this problem, we will use the formula for compound interest:
[tex]P_N=P_0\cdot(1+\frac{r}{k})^{N\cdot k}.[/tex]Where:
• P_N = principal amount after N years,
,• P_0 = initial principal amount,
,• r = interest ratio in decimals,
,• k = compound periods per year.
In this problem, we have:
• N = 9 years,
,• P_N = ?,
,• P_0 = $863,
,• r = 6.2% = 6.2/100 = 0.062,
,• k = 12 (the inerest is compounded monthly).
Replacing these data in the formula above, we get:
[tex]P_9=\text{ \$863 }\cdot(1+\frac{0.062}{12})^{9\cdot12}\cong\text{ \$1505.65.}[/tex]Answer
The balance after 9 years will be $1505.65 to the nearest cent.
