Answer:
To find the final balance of an account earning interest compounded continuously, you can use the formula:
A = Pe^(rt)
where A is the final account balance, P is the initial principal (or starting) amount, r is the interest rate, and t is the time (in years) for which the interest is being calculated.
Substituting in the given values:
A = 550 * e^(0.066 * 10)
Therefore, the final balance would be approximately $1064.14.
Answer:
C) $1064.14
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
Given:
Substitute the given values into the continuous compounding formula and solve for A:
[tex]\implies A=550e^{0.066 \times 10}[/tex]
[tex]\implies A=550e^{0.66}[/tex]
[tex]\implies A=550(1.93479233...)[/tex]
[tex]\implies A=1064.13578...[/tex]
Therefore, the balance of the account after 10 years would be $1064.14.
