Question

Edgar accumulated $5,000 in credit card debt. If the interest rate is 20% per year, and he does not make any payments for 2 years, how much will he owe on this debt in 2 years by each method of compounding? Round your answer to the nearest cent with no commas or dollar signs.

Compound continuously


7459.12


7237.12


7387.28


7434.57

Answer 1

To calculate the amount Edgar will owe after 2 years with continuous compounding, we can use the formula for continuous compounding:

\[ A = P e^{rt} \]

Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the time the money is invested or borrowed for, in years.
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).

Given:
- \( P = 5000 \)
- \( r = 0.20 \) (20% as a decimal)
- \( t = 2 \)

Now, substituting the given values into the formula:

\[ A = 5000 \times e^{0.20 \times 2} \]
\[ A = 5000 \times e^{0.40} \]

Now, calculate \( e^{0.40} \):

Using a calculator or a mathematical software, we find that

\[ e^{0.40} \approx 1.49182 \]

Now, multiplying by the principal amount:

\[ A \approx 5000 \times 1.49182 \]
\[ A \approx 7459.10 \]

Rounding to the nearest cent, Edgar will owe approximately \( 7459.10 \) after 2 years.

Among the options you've provided, the closest answer appears to be:

**7459.12**.