 DATOS	Interbank	BCP	BBVA
Va	6000	2827	4753
Vf	6847	3180	5161
N	?	?	?
i	16.53%	8.90%	10.50%
I
	?	?	?
 


To solve for the missing values in your table, we will use the formula for compound interest. The formula for the future value (Vf) of an investment is:

\[ Vf = Va \times (1 + i)^N \]

where:
- \( Vf \) is the future value
- \( Va \) is the present value (initial investment)
- \( i \) is the interest rate per period
- \( N \) is the number of periods

We can rearrange this formula to solve for \( N \):

\[ N = \frac{\log(\frac{Vf}{Va})}{\log(1 + i)} \]

Given dataTo solve for the missing values in your table, we will use the formula for compound interest. The formula for the future value (Vf) of an investment is:

\[ Vf = Va \times (1 + i)^N \]

where:
- \( Vf \) is the future value
- \( Va \) is the present value (initial investment)
- \( i \) is the interest rate per period
- \( N \) is the number of periods

We can rearrange this formula to solve for \( N \):

\[ N = \frac{\log(\frac{Vf}{Va})}{\log(1 + i)} \]

Given 
- Interbank: \( Va = 6000 \), \( Vf = 6847 \), \( i = 16.53\% \)
- BCP: \( Va = 2827 \), \( Vf = 3180 \), \( i = 8.90\% \)
- BBVA: \( Va = 4753 \), \( Vf = 5161 \), \( i = 10.50\% \)

### Calculations

#### For Interbank
\[ N_{Interbank} = \frac{\log(\frac{6847}{6000})}{\log(1 + 0.1653)} \]

#### For BCP
\[ N_{BCP} = \frac{\log(\frac{3180}{2827})}{\log(1 + 0.0890)} \]

#### For BBVA
\[ N_{BBVA} = \frac{\log(\frac{5161}{4753})}{\log(1 + 0.1050)} \]

Now let's calculate these values.

### Calculation Results

#### Interbank
\[ N_{Interbank} = \frac{\log(\frac{6847}{6000})}{\log(1 + 0.1653)} = \frac{\log(1.1412)}{\log(1.1653)} \approx \frac{0.056}{0.068} \approx 0.82 \text{ periods} \]

#### BCP
\[ N_{BCP} = \frac{\log(\frac{3180}{2827})}{\log(1 + 0.0890)} = \frac{\log(1.1246)}{\log(1.0890)} \approx \frac{0.050}{0.036} \approx 1.39 \text{ periods} \]

#### BBVA
\[ N_{BBVA} = \frac{\log(\frac{5161}{4753})}{\log(1 + 0.1050)} = \frac{\log(1.0858)}{\log(1.1050)} \approx \frac{0.036}{0.040} \approx 0.9 \text{ periods} \]

Let's summarize these results in the table.

|               | Interbank | BCP    | BBVA   |
|---------------|-----------|--------|--------|
| Va            | 6000      | 2827   | 4753   |
| Vf            | 6847      | 3180   | 5161   |
| N             | 0.82      | 1.39   | 0.9    |
| i             | 16.53%    | 8.90%  | 10.50% |

If you need to calculate the interest earned (I), we use the formula:

\[ I = Vf - Va \]

So:

- **Interbank**: \( I = 6847 - 6000 = 847 \)
- **BCP**: \( I = 3180 - 2827 = 353 \)
- **BBVA**: \( I = 5161 - 4753 = 408 \)

Updated table:

|               | Interbank | BCP    | BBVA   |
|---------------|-----------|--------|--------|
| Va            | 6000      | 2827   | 4753   |
| Vf            | 6847      | 3180   | 5161   |
| N             | 0.82      | 1.39   | 0.9    |
| i             | 16.53%    | 8.90%  | 10.50% |
| I             | 847       | 353    | 408    |

Would you like further details or have any questions?

Here are 5 questions you can ask next:
1. How do you derive the logarithm in these equations?
2. Can you explain the concept of compound interest in more detail?
3. What would happen if the interest rate changed midway through the period?
4. How can we apply these calculations to different financial products?
5. What are the implications of different compounding periods (e.g., monthly vs. annually)?

Tip: Always double-check your calculations, especially when dealing with exponential functions and logarithms, as small errors can lead to significant differences in the results.

Learn how to calculate compound interest and future values for financial investments in Interbank, BCP, and BBVA. Solve for missing periods (N) using logarithms and compound interest formulas with given data. Includes detailed calculations and results.

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