Directions - Use the continuous compound interest formula to calculate the final balance.

Question

Compound Interest Formula:
A
=
P
e
r
t
A=Pe
rt


$300 compounded continuously at 5% for 8 years.

Final balance = $
(if necessary, round to two decimal places)

Answer 1

To calculate the final balance using the continuous compound interest formula \( A = Pe^{rt} \), where:

• \( A \) = the final amount (balance)
• \( P \) = the principal (initial amount)
• \( r \) = the interest rate (as a decimal)
• \( t \) = the time in years
• \( e \) = the base of the natural logarithm (approximately equal to 2.71828)

Given the values:

• \( P = 300 \)
• \( r = 5% = 0.05 \)
• \( t = 8 \) years

We can substitute the values into the formula:

\[ A = 300 e^{0.05 \cdot 8} \]

First, calculate \( 0.05 \cdot 8 \):

\[ 0.05 \cdot 8 = 0.4 \]

Now we can find \( e^{0.4} \):

Using a scientific calculator or software, we find:

\[ e^{0.4} \approx 1.49182 \]

Now substitute this value back into the formula:

\[ A = 300 \times 1.49182 \]

Calculating this gives:

\[ A \approx 447.546 \]

Finally, rounding to two decimal places:

\[ A \approx 447.55 \]

So the final balance is $447.55.