To solve the problem of finding the Annual Percentage Rate (APR) for the loan:

Given Data:

• Principal (P) = $10,000
• Total Pay-out (A) = $15,000
• Time (T) = 5 years

We know the total interest ($I$) can be found as:
$I = A - P = 15,000 - 10,000 = 5,000$

The formula for simple interest is: $I = P \cdot r \cdot T$ where:

• $I$ is the interest
• $P$ is the principal
• $r$ is the annual interest rate (APR in decimal form)
• $T$ is the time (in years)

Substitute the values: $5,000 = 10,000 \cdot r \cdot 5$

Solve for $r$: $r = \frac{5,000}{10,000 \cdot 5} = 0.1$

Convert $r$ to a percentage: $\text{APR} = 0.1 \cdot 100 = 10\%$

Final Answer:

The APR charged on the loan is 10%.

Would you like me to explain this further or provide additional insights?

5 Related Questions:

1. How does simple interest differ from compound interest?
2. What would the APR be if the pay-out was $12,000 instead of $15,000?
3. How can the formula for simple interest be rearranged to find time instead of APR?
4. What is the total amount paid if the loan term is extended by 3 more years with the same APR?
5. How can understanding APR help in comparing loan options?

Tip:

Always ensure to differentiate between simple interest and compound interest, as the calculations and outcomes differ significantly.