Pedro opened a savings account and deposited $2,000.00. The account earns 8% interest, compounded monthly. If he wants to use the money to buy a new bicycle in 3 years, how much will he be able to spend on the bike?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.

To calculate how much Pedro will be able to spend on the bicycle in 3 years, we can use the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the final amount (what Pedro will have in the account after 3 years),
- $ P $ is the principal (the initial deposit of \$2000),
- $ r $ is the annual interest rate expressed as a decimal (8% = 0.08),
- $ n $ is the number of times the interest is compounded per year (monthly, so $ n = 12 $),
- $ t $ is the time in years (3 years).

Now, we can plug in the values:

\[
A = 2000 \left(1 + \frac{0.08}{12}\right)^{12 \times 3}
\]

Let me calculate that for you.After 3 years, Pedro will have approximately \$2,540.47 in his account, which he can use to buy the bicycle.

Would you like more details or have any questions? Here are 5 related questions:

1. How much interest does Pedro earn after 3 years?
2. What would the balance be if the interest rate was 6% instead of 8%?
3. How would the result change if the interest were compounded quarterly instead of monthly?
4. What is the formula for simple interest, and how does it differ from compound interest?
5. How long would it take for Pedro's money to double at this interest rate?

**Tip:** When calculating compound interest, the frequency of compounding has a significant impact on the final amount. More frequent compounding results in higher returns.

Pedro opened a savings account and deposited $2,000.00. The account earns 8% interest, compounded monthly. If he wants to use the money to buy a new bicycle in 3 years, how much will he be able to spend on the bike? Use the formula A = P(1 + r/n)^(nt), where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.

Discover how to calculate the final amount Pedro will have in his savings account after 3 years with an 8% interest rate, compounded monthly. This problem involves using the compound interest formula and is ideal for students in Grades 9-12.

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