Question

An account earning 6.6% interest compounded continuously for 10 years would have a balance

of how much if the principal was $550.
$984.96
$1046.41
O$1064.14

Answer 1

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 2

C) $1064.14

Explanation:

`\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}}`

Given:

• P = $550
• r = 6.6% = 0.066
• t = 10 years

Substitute the given values into the continuous compounding formula and solve for A:

`\implies A=550e^(0.066 * 10)`

`\implies A=550e^(0.66)`

`\implies A=550(1.93479233...)`

`\implies A=1064.13578...`

Therefore, the balance of the account after 10 years would be $1064.14.