To solve this problem, we will use the formula for simple interest, which is:

$I = P \times r \times t$

Where:

• $I$ is the interest,
• $P$ is the principal amount (the amount borrowed),
• $r$ is the annual interest rate (expressed as a decimal),
• $t$ is the time in years.

a) How much will the interest amount to?

1. Principal ($P$) = $500
2. Annual interest rate ($r$) = 6.6% = 0.066
3. Time ($t$) = 6 months = $\frac{6}{12}$ = 0.5 years

Now, calculate the interest: $I = 500 \times 0.066 \times 0.5 = 16.50$

So, the interest will amount to $16.50.

b) What amount must Miguel pay Julio at the end of 6 months?

The total amount Miguel must pay is the sum of the principal and the interest: $\text{Total amount} = P + I = 500 + 16.50 = 516.50$

Thus, Miguel must pay $516.50 at the end of 6 months.

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Do you want more details or have any questions?

Here are 5 related questions you could explore:

1. How would the interest change if the loan duration was 9 months instead of 6?
2. What if the interest rate was compounded instead of simple interest?
3. How would the interest calculation differ if Miguel paid monthly instead of after 6 months?
4. How does simple interest differ from compound interest in long-term loans?
5. How would the calculation change if the interest rate was 7.5%?

Tip: Always express the interest rate as a decimal in the formula by dividing the percentage by 100.