To solve this problem, we can use the compound interest formula:

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

Where:

• $A$ is the amount of money owed at the end of the loan period.
• $P$ is the principal amount (the initial loan), which is $50,000.
• $r$ is the annual interest rate (7% or 0.07).
• $n$ is the number of times the interest is compounded per year (weekly compounding means 52 times per year).
• $t$ is the time the money is borrowed for (3 years).

Now, substituting the given values:

$A = 50,000 \left(1 + \frac{0.07}{52}\right)^{52 \times 3}$

First, calculate the value of $\frac{0.07}{52}$:

$\frac{0.07}{52} = 0.0013461538$

Now calculate the exponent $52 \times 3 = 156$.

So, we now have:

$A = 50,000 \left(1 + 0.0013461538\right)^{156}$

$A = 50,000 \left(1.0013461538\right)^{156}$

Next, calculate $1.0013461538^{156}$:

$1.0013461538^{156} \approx 1.233004$

Now, calculate the total amount owed:

$A = 50,000 \times 1.233004 \approx 61,650.20$

Thus, the amount of money owed at the end of 3 years is approximately $61,650.20.

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Would you like more details on how the calculation works or have any questions? Here are some related questions you might find helpful:

1. What would the total amount owed be if the loan had a 5% interest rate compounded weekly?
2. How does the number of compounding periods per year (e.g., weekly vs. annually) affect the total amount owed?
3. How would the total amount change if the interest were compounded monthly instead of weekly?
4. What is the difference between simple interest and compound interest?
5. How would the loan amount change if the borrowing period was extended to 5 years?

Tip: The more frequently the interest is compounded, the greater the total interest paid over time.