You Save Bank has a unique account. If you deposit $7,000 today, the bank will pay you an annual interest rate of 3 percent for 4 years, 3.6 percent for 3 years, and 4.3 percent for 7 years. How much will you have in your account in 14 years? (Assume annual compounding.)

Multiple Choice

$9,082.51


$11,221.33


$10,588.13


$11,762.95


$9,939.83

To solve this problem, we will calculate the future value of the $7,000 deposit after 14 years, using the given interest rates for the different periods of time. Since the bank applies different interest rates over different time intervals, we need to break the problem down into three stages.

1. **For the first 4 years at 3% interest rate:**
   \[
   \text{Future Value for 4 years} = 7000 \times (1 + 0.03)^4
   \]

2. **For the next 3 years at 3.6% interest rate:**
   The amount from step 1 becomes the new principal for the next 3 years.
   \[
   \text{Future Value for next 3 years} = \text{Future Value from step 1} \times (1 + 0.036)^3
   \]

3. **For the final 7 years at 4.3% interest rate:**
   The amount from step 2 becomes the new principal for the next 7 years.
   \[
   \text{Future Value for next 7 years} = \text{Future Value from step 2} \times (1 + 0.043)^7
   \]

Now, let's compute the final future value.The total amount in your account after 14 years will be **$11,762.95**, which corresponds to the last option in the multiple choices provided.

Would you like more details or have any further questions? Here are five related questions to consider:

1. What is the formula for calculating compound interest?
2. How does the frequency of compounding affect the future value?
3. What is the impact of increasing the interest rate by 1% over the same period?
4. How does the future value change if the time period increases to 20 years?
5. How would the calculation differ with monthly compounding instead of annual?

**Tip:** The power of compounding increases with time and higher interest rates, making long-term investments grow faster.

You Save Bank has a unique account. If you deposit $7,000 today, the bank will pay you an annual interest rate of 3 percent for 4 years, 3.6 percent for 3 years, and 4.3 percent for 7 years. How much will you have in your account in 14 years? (Assume annual compounding.)

Learn how to calculate the future value of a $7,000 deposit over 14 years with varying interest rates of 3%, 3.6%, and 4.3%. This problem covers the concept of compound interest, using step-by-step formulas for each interest period. Suitable for students in Grades 10-12.

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