Kathy borrows $5600 in her first year of college. How much will she owe at the end of 5 years if her loan is at 13.0% per year, compounded monthly?

Enter a numeric value rounded to the nearest hundredth, with no dollar sign and no spaces.

An answer of $100 should be entered as 100.00

To determine how much Kathy will owe at the end of 5 years with a loan at 13.0% per year, compounded monthly, we can use the formula for compound interest:

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

where:
- $ A $ is the amount of money accumulated after n years, including interest.
- $ P $ is the principal amount (the initial amount of money, which is $5600).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested for in years.

Given:
- $ P = 5600 $
- $ r = 0.13 $
- $ n = 12 $ (since the interest is compounded monthly)
- $ t = 5 $

First, we calculate the monthly interest rate:
\[ \frac{r}{n} = \frac{0.13}{12} \approx 0.0108333 \]

Next, we calculate the total number of compounding periods:
\[ nt = 12 \times 5 = 60 \]

Now we can plug these values into the compound interest formula:
\[ A = 5600 \left(1 + 0.0108333\right)^{60} \]

Let's calculate this step-by-step:

1. Calculate $ 1 + \frac{r}{n} $:
\[ 1 + 0.0108333 = 1.0108333 \]

2. Raise this to the power of $ nt $:
\[ 1.0108333^{60} \approx 1.888487 \]

3. Multiply this by the principal amount $ P $:
\[ 5600 \times 1.888487 \approx 10575.52 \]

Therefore, the amount Kathy will owe at the end of 5 years is:
\[ \boxed{10575.52} \]

Do you want details or have any questions?

Here are 5 more questions you might be interested in:
1. How do you calculate the effective annual rate (EAR) for a given nominal interest rate compounded monthly?
2. What is the formula for continuous compound interest and how does it differ from regular compound interest?
3. How can you calculate the future value of an annuity with monthly contributions?
4. How do you determine the present value of a future sum of money given a specific interest rate and time period?
5. How do you solve for the interest rate in a compound interest problem if the other variables are known?

**Tip:** Always make sure to convert the annual interest rate to the appropriate period rate when dealing with compounded interest calculations.

Learn how to calculate compound interest with monthly compounding for Kathy's $5600 college loan at 13.0% per year over 5 years. Get a detailed step-by-step solution with precise calculations and formula application.

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