Tony DeMarco is saving for a computer. At the beginning of each month, he puts
$60 in a savings account that pays 8% interest compounded monthly. How much
is in the account after three years?

To calculate the amount in Tony DeMarco's savings account after three years, we can use the future value of an annuity formula. Since the interest is compounded monthly, the formula is:

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

Where:
- $ FV $ is the future value of the annuity (the amount in the account after three years).
- $ P $ is the monthly payment (\$60).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the total number of payments (number of months).

Given:
- Annual interest rate $ = 8\% $ or $ 0.08 $ as a decimal.
- Monthly interest rate $ r = \frac{0.08}{12} = 0.0066667 $.
- Number of months $ n = 3 \times 12 = 36 $.

Now, substituting these values into the formula:

\[
FV = 60 \times \frac{(1 + 0.0066667)^{36} - 1}{0.0066667}
\]

Let's calculate this value.The amount in Tony DeMarco's savings account after three years will be approximately **$2,432.13**.

Would you like to know more details or have any questions?

Here are 5 related questions to expand on this topic:
1. How would the final amount change if Tony saved $100 each month instead of $60?
2. What would be the future value if the interest rate were 10% instead of 8%?
3. How much interest did Tony earn over the three years?
4. What would the future value be if the interest were compounded quarterly instead of monthly?
5. How would the total savings change if the saving period were extended to 5 years?

**Tip:** When saving regularly, the frequency of compounding can significantly impact the total amount accumulated over time.

Learn how to calculate the amount in Tony DeMarco's savings account after three years with compound interest. This problem involves monthly savings, an 8% annual interest rate compounded monthly, and uses the Future Value of Annuity formula. Discover how different factors affect the final savings amount.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation