1- Calcule el monto, en cada uno de los siguientes casos: a) $ 1.500.000 al 18% anual a 180 días de plazo, b) $ 2.800.000 al 1,7% mensual a 120 días plazo, c) $ 5.000.000 al 9% anual del 15 de marzo
al 31 de agosto del mismo año, d) $ 8.500.000 al 14,5% anual del 10 de agosto al 15 de diciembre del mismo año.

To calculate the final amount (`monto`) in each case, we use the formula for simple interest when the interest isn't compounded over the period:

\[
M = P \left(1 + \frac{r \cdot t}{100}\right)
\]

where:
- $M$ is the total amount after time $t$,
- $P$ is the principal amount (initial investment),
- $r$ is the interest rate (as a percentage),
- $t$ is the time period in years.

Let's solve each sub-problem:

### a) $1,500,000 at 18% annual interest for 180 days:

Convert 180 days to years:

\[
t = \frac{180}{360} = 0.5 \text{ years}
\]

The interest rate $r = 18\%$.

\[
M = 1,500,000 \left(1 + \frac{18 \times 0.5}{100}\right)
\]

\[
M = 1,500,000 \left(1 + 0.09\right) = 1,500,000 \times 1.09
\]

\[
M = 1,635,000
\]

**The amount is $1,635,000.**

### b) $2,800,000 at 1.7% monthly interest for 120 days:

Convert 120 days to months, given there are approximately 30 days in a month:

\[
t = \frac{120}{30} = 4 \text{ months}
\]

Since the interest rate is monthly at $1.7\%$, we calculate:

\[
M = 2,800,000 \left(1 + \frac{1.7 \times 4}{100}\right)
\]

\[
M = 2,800,000 \left(1 + 0.068\right) = 2,800,000 \times 1.068
\]

\[
M = 2,990,400
\]

**The amount is $2,990,400.**

### c) $5,000,000 at 9% annual interest from March 15 to August 31:

Calculate the number of days from March 15 to August 31:

- March 15 to March 31: 16 days
- April: 30 days
- May: 31 days
- June: 30 days
- July: 31 days
- August: 31 days

Total days = $16 + 30 + 31 + 30 + 31 + 31 = 169$ days.

Convert days to years:

\[
t = \frac{169}{360} \approx 0.4694 \text{ years}
\]

Annual interest rate $r = 9\%$.

\[
M = 5,000,000 \left(1 + \frac{9 \times 0.4694}{100}\right)
\]

\[
M = 5,000,000 \left(1 + 0.042246\right) = 5,000,000 \times 1.042246
\]

\[
M \approx 5,211,230
\]

**The amount is approximately $5,211,230.**

### d) $8,500,000 at 14.5% annual interest from August 10 to December 15:

Calculate the number of days from August 10 to December 15:

- August 10 to August 31: 21 days
- September: 30 days
- October: 31 days
- November: 30 days
- December 1 to December 15: 15 days

Total days = $21 + 30 + 31 + 30 + 15 = 127$ days.

Convert days to years:

\[
t = \frac{127}{360} \approx 0.3528 \text{ years}
\]

Annual interest rate $r = 14.5\%$.

\[
M = 8,500,000 \left(1 + \frac{14.5 \times 0.3528}{100}\right)
\]

\[
M = 8,500,000 \left(1 + 0.051156\right) = 8,500,000 \times 1.051156
\]

\[
M \approx 8,934,826
\]

**The amount is approximately $8,934,826.**

---

Would you like more details on any specific calculation, or do you have any questions? Here are some related questions to consider:

1. How would these calculations change if interest was compounded monthly instead of annually?
2. What is the difference between simple interest and compound interest in terms of calculation?
3. How does the number of days in a year (360 vs. 365) affect these interest calculations?
4. How can you determine which investment option is better when comparing different interest rates and compounding periods?
5. Why is it important to convert the time period into years when calculating annual interest?

**Tip:** Always remember to convert the time period to years when working with annual interest rates, and to months or days as needed for monthly or daily rates.

Learn how to calculate the final amount in financial scenarios using simple interest. Explore examples like $1,500,000 at 18% annual interest for 180 days, $2,800,000 at 1.7% monthly interest for 120 days, $5,000,000 at 9% annual interest from March 15 to August 31, and $8,500,000 at 14.5% annual interest from August 10 to December 15.

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