type the correct answer in the box. round your answer to the nearest whole number.\nandrew deposited $500 in…

type the correct answer in the box. round your answer to the nearest whole number.\nandrew deposited $500 in a savings account that offers an interest rate of 6.5%, compounded continuously.\nandrews initial deposit will grow to about $543 in months.

Answer

Explanation:

Step1: Recall continuous compound formula

The formula for continuous compounding is $A = Pe^{rt}$, where:

$A = 543$ (final amount),
$P = 500$ (principal),
$r = 0.065$ (annual interest rate),
$t$ = time in years.

Step2: Isolate the exponential term

Divide both sides by $P$: $\frac{A}{P} = e^{rt}$ Substitute values: $\frac{543}{500} = e^{0.065t}$ Simplify left side: $1.086 = e^{0.065t}$

Step3: Convert to logarithmic form

Take natural log of both sides: $\ln(1.086) = 0.065t$

Step4: Solve for t in years

Rearrange to solve for $t$: $t = \frac{\ln(1.086)}{0.065}$ Calculate: $\ln(1.086) \approx 0.0825$, so $t \approx \frac{0.0825}{0.065} \approx 1.269$ years

Step5: Convert years to months

Multiply by 12: $t_{months} = 1.269 \times 12 \approx 15.23$ Round to nearest whole number.