Question

Edgar accumulated 5,000
in credit card debt. If the interest rate is 20% 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 quarterly


7387.28


7237.12


7459.12


7434.57

Answer 1

To calculate the amount owed after 2 years with compound interest compounded quarterly, we can use the formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

where:
- \( A \) is the amount owed after time \( t \),
- \( P \) is the principal amount (initial debt),
- \( r \) is the annual interest rate (decimal),
- \( n \) is the number of times interest is compounded per year,
- \( t \) is the time in years.

Given:
- \( P = 5000 \)
- \( r = 0.20 \) (20%)
- \( n = 4 \) (quarterly)
- \( t = 2 \)

Now, substituting the values into the formula:

\[
A = 5000 \left(1 + \frac{0.20}{4}\right)^{4 \times 2}
\]

Calculating:

1. Calculate \(\frac{0.20}{4}\):

\[
\frac{0.20}{4} = 0.05
\]

2. Substitute back into the formula:

\[
A = 5000 \left(1 + 0.05\right)^{8}
\]

3. Calculate \(1 + 0.05\):

\[
1 + 0.05 = 1.05
\]

4. Now we find \(A\):

\[
A = 5000 \left(1.05\right)^{8}
\]

Calculating \(1.05^8\):

\[
1.05^8 \approx 1.477455
\]

5. Now multiply by the principal:

\[
A \approx 5000 \times 1.477455 \approx 7387.28
\]

Therefore, the total amount owed after 2 years, compounded quarterly, is **7387.28**.