Brendan opened a savings account and deposited $700.00. The account earns 12% 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?

We can solve this problem using the compound interest formula:

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

Where:
- $A$ = the amount of money in the account after interest
- $P$ = the initial principal (amount deposited), which is \$700
- $r$ = the annual interest rate (12%, or 0.12)
- $n$ = the number of times the interest is compounded per year (monthly compounding, so $n = 12$)
- $t$ = the time the money is invested for, in years (3 years)

### Step 1: Plug the values into the formula

\[
A = 700 \left(1 + \frac{0.12}{12}\right)^{12 \times 3}
\]

\[
A = 700 \left(1 + 0.01\right)^{36}
\]

\[
A = 700 \left(1.01\right)^{36}
\]

### Step 2: Calculate the exponent

Now, let's calculate $A$.

\[
A = 700 \times 1.432364654
\]

\[
A \approx 1002.66
\]

Brendan will have approximately \$1002.66 after 3 years. This is the amount he can spend on a new bicycle.

Would you like more details or have any questions?

Here are 5 related questions to extend this topic:
1. How would the amount change if the interest rate was higher or lower?
2. What if the interest was compounded quarterly instead of monthly?
3. How much would Brendan have if he deposited additional money each year?
4. What happens if the time is increased to 5 years?
5. How would a one-time withdrawal affect the compound interest?

**Tip:** To get the best returns, always try to invest in accounts with higher compounding frequencies.

Find out how much Brendan will have saved after 3 years in a savings account with 12% interest, compounded monthly. This problem involves using the compound interest formula to calculate the total amount, making it ideal for students in Grades 9-12 learning about exponential growth and interest rates.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation