Question

Edgar accumulated $3,000 in credit card debt. If the interest rate is 20% per year and he does not make any payments for 5 years, how much will he owe on this debt in 5 years by compounding continuously?

Answer 1

The amount Edgar will owe on his credit card debt in 5 years by continuously compounding the interest is $8,154.84.

Step-by-step explanation:

To find how much Edgar will owe on his credit card debt in 5 years by continuously compounding the interest, we can use the formula for compound interest:

A = P * e^(rt)

where:

• A is the amount after time t
• P is the principal amount (the initial debt)
• r is the interest rate (in decimal form)
• t is the time in years
• e is the base of the natural logarithm (approximately 2.71828)

Plugging in the values from the question, we have:

A = 3000 * e^(0.2 * 5)

A = 3000 * e^1

Using a calculator, we can find that e^1 is approximately 2.71828.

So, the amount Edgar will owe on his credit card debt in 5 years by continuously compounding the interest is:

A = 3000 * 2.71828 = $8,154.84