Deposits of $58.00 are made at the end of every quarter for 10.5 years. What will the deposits amount to if interest is 4% compounded quarterly?
The future value is $(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

To calculate the future value of the deposits, we can use the future value formula for an ordinary annuity:

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

Where:
- $ FV $ is the future value of the annuity.
- $ P $ is the payment amount per period ($58.00).
- $ r $ is the interest rate per period.
- $ n $ is the total number of periods.

**Step 1: Identify the variables**

- The quarterly interest rate ($ r $) = $ \frac{4\%}{4} = 0.01 $ per quarter.
- The number of quarters ($ n $) = $ 10.5 \text{ years} \times 4 = 42 $ quarters.

**Step 2: Apply the values to the formula**

\[
FV = 58.00 \times \frac{(1 + 0.01)^{42} - 1}{0.01}
\]

**Step 3: Calculate the future value**

\[
FV = 58.00 \times \frac{(1.01)^{42} - 1}{0.01}
\]
\[
FV = 58.00 \times \frac{1.519026 - 1}{0.01}
\]
\[
FV = 58.00 \times \frac{0.519026}{0.01}
\]
\[
FV = 58.00 \times 51.9026
\]
\[
FV = 3004.3508
\]

**Step 4: Round to the nearest cent**

\[
FV \approx 3004.35
\]

The future value of the deposits is **$3,004.35**.

Would you like more details or have any other questions?

---

Here are 8 related questions to expand your understanding:
1. How does the interest rate affect the future value of an annuity?
2. What if the interest was compounded monthly instead of quarterly?
3. How would the future value change if the deposits were made at the beginning of each quarter?
4. How does changing the deposit amount to $100 affect the future value?
5. What is the difference between an ordinary annuity and an annuity due?
6. How do you calculate the present value of a series of payments?
7. How would the calculation change if the interest rate was 5% instead of 4%?
8. What if the deposits were made over 15 years instead of 10.5 years?

**Tip:** Always double-check the compounding period and the interest rate to ensure the correct application of the formula.

Learn how to calculate the future value of quarterly deposits of $58.00 over 10.5 years with a 4% interest rate compounded quarterly. This problem involves the application of compound interest and annuity formulas. Suitable for advanced high school students and college-level learners.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation