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To resolve the problem in the image, let's break down the details and perform a step-by-step comparison of the two investment plans mentioned. 

### Information provided:

1. **Fondo Realizar**:
   - Interest rates over 5 years are: 8%, 7%, 6%, 5%, and 4%.
   
2. **Fondo Crecer**:
   - Fixed annual nominal interest rate of 6%.

We need to determine which plan yields the higher return over the 5-year period by applying the appropriate financial formulas.

#### Approach:

We will compute the future value (FV) for each plan after 5 years.

### Plan 1: **Fondo Realizar**

The interest rates change every year, so we will calculate the compounded future value year by year using the formula:

\[
FV = PV \times (1 + r_1) \times (1 + r_2) \times \dots \times (1 + r_n)
\]

Where \( r_1, r_2, \dots, r_5 \) are the interest rates for each year.

\[
FV = PV \times (1 + 0.08) \times (1 + 0.07) \times (1 + 0.06) \times (1 + 0.05) \times (1 + 0.04)
\]

### Plan 2: **Fondo Crecer**

This plan has a fixed interest rate, so we use the standard compound interest formula:

\[
FV = PV \times (1 + r)^n
\]

Where \( r = 0.06 \) and \( n = 5 \):

\[
FV = PV \times (1 + 0.06)^5
\]

### Next Step:

We will calculate the future value of both plans assuming an initial investment \( PV \), then compare the results to determine the better option. Let me compute that now.The future values (FV) for both plans are as follows, assuming an initial investment of 1 unit:

1. **Fondo Realizar**: \( FV = 1.3376 \)
2. **Fondo Crecer**: \( FV = 1.3382 \)

### Conclusion:
The **Fondo Crecer** plan offers a slightly higher return (1.3382) compared to the **Fondo Realizar** plan (1.3376) over the 5-year period. Therefore, **Fondo Crecer** is the better option based on this comparison.

Would you like further details, or do you have any other questions? Here are some related questions to deepen your understanding:

1. How does the choice of investment period affect compound interest?
2. What happens if the interest rates were to decrease in the future for a similar plan?
3. How can inflation impact the real return on these types of investments?
4. Can we use the same method to evaluate monthly compounded interest?
5. How do nominal and effective interest rates differ?

**Tip**: When comparing investment plans with varying interest rates, it's essential to consider the compounding frequency and any potential fees or penalties that could impact the returns.

Take the better of the following five-year rent plans (without partial withdrawals of funds during the investment): - FONDO REALIZAR: Guarantees annual effective interest rates for each of the five following years in this order: 8%, 7%, 6%, 5%, 4%. - FONDO CRECER: Agrees on a fixed annual nominal interest rate of 6%. Note: Remember to use the formulas, develop the procedures, and justify your answer.

Explore a detailed comparison between two investment rent plans—Fondo Realizar with varying interest rates (8%, 7%, 6%, 5%, 4%) and Fondo Crecer with a fixed 6% rate. Understand the use of compound interest formulas to calculate the future value (FV) of these plans over a five-year period.

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