Jamie will deposit $50 each month into an account with an APR of 8% compounded monthly. Find the balance of Jamie's account after 45 years.


$365,872.66


$2,250


$263,726.99


$27,000


$450,982.38

To solve this problem, we need to use the formula for the future value of a series of regular deposits into an account with compound interest:

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

Where:
- $ A $ is the future value of the investment (the balance in Jamie's account),
- $ P $ is the regular deposit (in this case, $50 per month),
- $ r $ is the monthly interest rate (APR divided by 12),
- $ n $ is the total number of deposits (number of months).

### Step 1: Identify the values
- $ P = 50 $
- APR = 8% (so the monthly interest rate is $ \frac{8}{12} \div 100 = 0.00667 $)
- Time = 45 years (so the total number of months is $ 45 \times 12 = 540 $).

### Step 2: Plug these values into the formula
\[
A = 50 \times \left( \frac{{(1 + 0.00667)^{540} - 1}}{0.00667} \right)
\]

### Step 3: Calculate the future value
First, calculate the term inside the parentheses.

Now we can compute the balance in Jamie's account.

The correct balance will be closest to **$263,726.99**.

Would you like further details or a breakdown of the calculations?

Here are 5 relative questions:
1. What happens if the deposit amount is increased to $100 per month?
2. How does the balance change with a 6% APR instead of 8%?
3. What if Jamie deposits for 30 years instead of 45 years?
4. How does the frequency of compounding affect the final balance?
5. How would the balance differ if it was compounded quarterly?

**Tip**: Small changes in interest rates or compounding frequency can have a big impact over long periods of time!

Jamie will deposit $50 each month into an account with an APR of 8% compounded monthly. Find the balance of Jamie's account after 45 years.

Find out how to calculate the balance of Jamie's account after depositing $50 monthly for 45 years at an 8% APR compounded monthly. Using the compound interest formula, we calculate the future value of the investment, resulting in a balance of approximately $263,726.99. Ideal for high school students learning about compound interest and exponential growth.

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