Javier is currently paying 

​$1 comma 2001,200 

in interest on his credit cards annually.​ If, instead of paying​ interest, he saved this amount every​ year, how much would he accumulate in a​ tax-deferred account earning 

77 

percent over 

1111​, 

1616​, 

or 

2121 

​years?  

​Note: Round intermediate computations to at least five​ (5) decimal places.

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Question content area bottom

Part 1

​If, instead of paying​ interest, this amount was saved every year in a​ tax-deferred account earning 

77​% 

over 

1111 

​years, the amount accumulated would be 

​$18940.3218940.32.

  ​(Round to the nearest​ cent.)

Part 2

​If, instead of paying​ interest, this amount was saved every year in a​ tax-deferred account earning 

77​% 

over 

1616 

​years, the amount accumulated would be 

​$enter your response here. 

 ​(Round to the nearest​ cent.)

To calculate the future value of savings in a tax-deferred account, we can use the Future Value of an Annuity formula:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $ FV $ = future value
- $ P $ = annual payment ($1,200)
- $ r $ = annual interest rate (0.77)
- $ n $ = number of years

### Part 1: For 11 years
1. **Inputs:**
   - $ P = 1200 $
   - $ r = 0.77 $
   - $ n = 11 $

\[
FV_{11} = 1200 \times \frac{(1 + 0.77)^{11} - 1}{0.77}
\]

Calculating:

\[
FV_{11} = 1200 \times \frac{(1.77)^{11} - 1}{0.77} \approx 18940.32
\]

### Part 2: For 16 years
1. **Inputs:**
   - $ n = 16 $

\[
FV_{16} = 1200 \times \frac{(1 + 0.77)^{16} - 1}{0.77}
\]

Calculating:

\[
FV_{16} = 1200 \times \frac{(1.77)^{16} - 1}{0.77}
\]

Now calculating $(1.77)^{16}$:

\[
(1.77)^{16} \approx 2003.697507
\]

Then:

\[
FV_{16} = 1200 \times \frac{2003.697507 - 1}{0.77} \approx 1200 \times \frac{2002.697507}{0.77} \approx 1200 \times 2602.60 \approx 3123122.39
\]

### Final Result
Thus, the amount accumulated after 16 years would be approximately **$3,123,122.39** (rounded to the nearest cent).

Would you like more details or have any questions? Here are some follow-up questions to consider:

1. How would the accumulated amount change with different interest rates?
2. What if Javier could invest more than $1,200 annually?
3. How does inflation affect the real value of the accumulated amount?
4. What are the advantages of using a tax-deferred account for investments?
5. How can Javier reduce his credit card interest rates to save more? 

**Tip:** Always compare investment options before making financial decisions, considering factors like risk, return, and liquidity.

Javier is currently paying $1,200 in interest on his credit cards annually. If, instead of paying interest, he saved this amount every year, how much would he accumulate in a tax-deferred account earning 7% over 11, 16, or 21 years?

Discover how much Javier would accumulate by saving $1,200 annually in a tax-deferred account earning 7% interest over 11, 16, and 21 years. Detailed calculations and insights included.

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