Suppose that my bank account compounds monthly at an APR of 4.5%. If I haven’t touched the account since I made my initial deposit 14 years ago, how much money was in my account 4 years ago if my current balance is $3000? (round down to 2 decimal places)

The formula for compound interest is:

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

Where:
- $ A $ is the amount of money after interest (final balance),
- $ P $ is the principal (initial deposit),
- $ r $ is the annual interest rate (expressed as a decimal),
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the time the money has been in the account (in years).

### Given information:
- Current balance (4 years ago): $ A = 3000 $,
- APR (annual percentage rate): $ r = 4.5\% = 0.045 $,
- Compounded monthly, so $ n = 12 $,
- The total time since the initial deposit is 14 years. We want to find the balance 4 years ago, meaning the money was compounded for $ t = 10 $ years.

We need to first calculate $ P $, the initial deposit 14 years ago, and then use it to calculate the balance 4 years ago. To do that:

1. Rearrange the formula to solve for $ P $:

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

Let me calculate this.The balance in your account 4 years ago was approximately \$2506.65.

Would you like further details or have any other questions?

Here are 5 related questions to explore:
1. How much interest was earned in the last 4 years?
2. How would the balance change if the APR was higher, say 5%?
3. What would be the balance if it compounded daily instead of monthly?
4. How would the initial deposit affect the balance after 14 years?
5. What is the difference between simple and compound interest in this context?

**Tip:** Compounding more frequently (e.g., monthly instead of annually) increases the balance slightly over time.

Discover how to calculate the balance of a bank account that compounds monthly at an APR of 4.5% over 14 years, starting from an initial deposit. Learn the compound interest formula and solve for the balance 4 years ago given a current balance of $3000. Suitable for Grades 10-12.

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