You are planning to make annual deposits of $3,600 into a retirement account that pays 8 percent interest compounded monthly. How large will your account balance be in 25 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value

FINANCIAL ACCOUNTING
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Chapter1: Financial Statements And Business Decisions
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**Future Value and Retirement Planning**

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### Question:

You are planning to make annual deposits of $3,600 into a retirement account that pays 8 percent interest compounded monthly. How large will your account balance be in 25 years?

*(Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)*

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### Input Field:
- **Future value:** [__________]

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### Explanation:

This problem involves calculating the future value of an annuity where interest is compounded monthly. The future value (FV) of an annuity can be calculated using the following formula:

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

where:
- \( P \) = annual deposit ($3,600)
- \( r \) = annual interest rate (8%, or 0.08)
- \( n \) = number of times the interest is compounded per year (12 for monthly)
- \( t \) = number of years the money is invested (25)

By substituting the given values into the formula, you can compute the future value of the retirement account.

### Steps:

1. **Identify the parameters:**
   - Annual Deposit (P): $3,600
   - Annual Interest Rate (r): 0.08
   - Compounding Frequency per year (n): 12
   - Time in years (t): 25

2. **Calculate the monthly interest rate:**
   - Monthly interest rate = \( \frac{0.08}{12} \)

3. **Apply the future value formula for each year's annuity contribution:**
   - Calculate each term and sum them up to determine the total future value.

4. **Round to two decimal places:**
   - Ensure the final calculated amount is rounded to two decimal places for accuracy.

This approach will give you the precise amount that will be in your retirement account at the end of 25 years.
Transcribed Image Text:**Future Value and Retirement Planning** --- ### Question: You are planning to make annual deposits of $3,600 into a retirement account that pays 8 percent interest compounded monthly. How large will your account balance be in 25 years? *(Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)* --- ### Input Field: - **Future value:** [__________] --- ### Explanation: This problem involves calculating the future value of an annuity where interest is compounded monthly. The future value (FV) of an annuity can be calculated using the following formula: \[ FV = P \times \left( \frac{(1 + r/n)^{nt} - 1}{r/n} \right) \] where: - \( P \) = annual deposit ($3,600) - \( r \) = annual interest rate (8%, or 0.08) - \( n \) = number of times the interest is compounded per year (12 for monthly) - \( t \) = number of years the money is invested (25) By substituting the given values into the formula, you can compute the future value of the retirement account. ### Steps: 1. **Identify the parameters:** - Annual Deposit (P): $3,600 - Annual Interest Rate (r): 0.08 - Compounding Frequency per year (n): 12 - Time in years (t): 25 2. **Calculate the monthly interest rate:** - Monthly interest rate = \( \frac{0.08}{12} \) 3. **Apply the future value formula for each year's annuity contribution:** - Calculate each term and sum them up to determine the total future value. 4. **Round to two decimal places:** - Ensure the final calculated amount is rounded to two decimal places for accuracy. This approach will give you the precise amount that will be in your retirement account at the end of 25 years.
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