Answer:
[tex]\boxed {\boxed {\sf \$9,534.37}}[/tex]
Step-by-step explanation:
The formula for continuously compounded is:
[tex]A=Pe^{rt}[/tex]
where P is the principal amount, r is the interest rate as a decimal, and t is the amount of time.
The principal amount is $7,500 and time is 16 years. The interest rate is 1.5%. Convert this to a decimal- divide by 100 or move the decimal places two spots to the left.
Now we know all the values and can substitute them into the formula.
[tex]P= 7500 \\r= 0.015 \\t= 16[/tex]
[tex]A= 7500(e^{0.015*16})[/tex]
Solve the multiplication in the exponent first.
[tex]A= 7500(e^{24})[/tex]
Solve the exponent.
[tex]A= 7500 (1.27124915)[/tex]
[tex]A=9534.368627[/tex]
Round to the nearest cent (hundredth place). The 8 in the thousandth place tells us to the round the 6 to a 7.
[tex]A=9534.37[/tex]
The account balance will be $9,534.37 after 16 years.
