The information we have is:
Principal, the invested amount:
[tex]P=89,000[/tex]Interest rate:
[tex]r=3.1\text{ percent }[/tex]We will need the percent as a decimal, so we divide by 100:
[tex]r=0.031[/tex]Time of the investment in years:
[tex]t=15[/tex]Since the investment is compounded continuously, we need to use the formula for continuous compounding:
[tex]A=Pe^{rt}[/tex]Where P, r, and t are the values we defined earlier. And A is the Amount after 15 years. Also, e is a mathematical constant:
[tex]e=2.7183[/tex]Substituting these values into the formula:
[tex]A=(89,000)(2.7183)^{(0.031\times15)}[/tex]Solving the operations:
[tex]\begin{gathered} A=(89,000)(2.7183)^{(0.465)} \\ A=(89,000)(2.7183)^{(0.465)} \\ A=(89,000)(1.592) \\ A=141,689.7 \end{gathered}[/tex]Answer: $141,689.7
To round the answer to the nearest ten dollars, we should round the last three digits: 89.7 to the nearest tens which is 90.
So the rounded answer will be: $141,690
