Reagan puts $200.00 into an account to use for school expenses. The account earns 11% interest, compounded annually. How much will be in the account after 5 years?

Use the formula 

A

=

P

1

+

r

n

n

t

,

 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 the amount in Reagan's account after 5 years, we can use the compound interest formula:

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

where:
- $ A $ is the balance (final amount),
- $ P $ is the principal (initial amount), which is $200,
- $ r $ is the interest rate as a decimal, which is 11%, or 0.11,
- $ n $ is the number of times per year the interest is compounded, which is 1 (since it’s compounded annually),
- $ t $ is the time in years, which is 5.

### Step 1: Substitute the values into the formula.

\[
A = 200 \left(1 + \frac{0.11}{1}\right)^{1 \times 5}
\]

### Step 2: Simplify inside the parentheses.

\[
A = 200 \left(1 + 0.11\right)^5
\]
\[
A = 200 \times (1.11)^5
\]

### Step 3: Calculate $ (1.11)^5 $.

\[
(1.11)^5 \approx 1.6851
\]

### Step 4: Multiply by the principal.

\[
A = 200 \times 1.6851 \approx 337.02
\]

### Final Answer:
The amount in the account after 5 years will be **$337.02**.

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

Here are 5 related questions:
1. How much would Reagan have after 5 years if the interest rate were 12%?
2. What would the balance be if the interest were compounded semiannually instead of annually?
3. How would the amount change if Reagan left the money in the account for 10 years?
4. What if Reagan deposited $300 instead of $200 initially?
5. How much interest would Reagan earn if the interest was compounded monthly?

**Tip:** Compounding frequency can make a significant difference; the more frequently interest is compounded, the greater the total amount over time.

Reagan puts $200.00 into an account to use for school expenses. The account earns 11% interest, compounded annually. How much will be in the account after 5 years? 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.

Learn how to calculate compound interest on a $200 deposit with an 11% annual interest rate, compounded annually, over 5 years. This problem demonstrates exponential growth and applies the compound interest formula, suitable for high school math students in Grades 9-12.

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