Roofs and HVAC units are two of the most expensive investments for homeowners (a basic
HVAC unit costs about $7,000). Suppose Mr. Nunez is saving for a HVAC unit by depositing $500 a quarter into an account that earns 4.75% quarterly. How much will be in this account after 20 years (the average lifespan of a HVAC unit)?

We can solve this problem using the **future value of an ordinary annuity formula**, since Mr. Nunez is making regular deposits of $500 each quarter:

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

Where:
- $FV$ = Future value of the account
- $P$ = Payment amount each quarter ($500)
- $r$ = Quarterly interest rate
- $n$ = Total number of periods (quarters)

### Given values:
- $P = 500$ (deposit per quarter)
- The annual interest rate is 4.75%, but since the interest compounds quarterly, the **quarterly interest rate** is:
  \[
  r = \frac{4.75\%}{4} = \frac{0.0475}{4} = 0.011875
  \]
- The time period is 20 years. Since there are 4 quarters in a year, the total number of quarters is:
  \[
  n = 20 \times 4 = 80 \text{ quarters}
  \]

Now, let's calculate the future value using these inputs.The future value of the account after 20 years will be approximately **$66,159.14**.

Would you like further details on this calculation or have any other questions?

Here are 5 related questions you may find useful:
1. What is the difference between simple interest and compound interest?
2. How does the frequency of compounding affect the future value of an investment?
3. What happens if Mr. Nunez increases his quarterly deposits?
4. How would inflation affect the purchasing power of the saved amount after 20 years?
5. How can Mr. Nunez calculate the future value of other long-term savings goals?

**Tip:** Increasing the frequency of your deposits or reducing the time between them can significantly increase the future value of your investments due to compounding effects.

Roofs and HVAC units are two of the most expensive investments for homeowners (a basic HVAC unit costs about $7,000). Suppose Mr. Nunez is saving for a HVAC unit by depositing $500 a quarter into an account that earns 4.75% quarterly. How much will be in this account after 20 years (the average lifespan of a HVAC unit)?

Learn how to calculate the future value of savings for an HVAC unit using the compound interest formula. This problem covers key financial concepts like future value, annuities, and compound interest rates, and is suitable for students in Grades 11-12. The solution shows that Mr. Nunez will have approximately $66,159.14 after 20 years of saving $500 quarterly with a 4.75% interest rate.

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