Suppose that my bank account compounds monthly at an APR of 4.6%. If I haven’t touched the account since I made my initial deposit 15 years ago, how much money was in my account 4 years ago if my current balance is $4000? (round down to 2 decimal places) 

To solve this problem, we need to use the formula for compound interest, which is:

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

Where:
- $A$ is the amount of money in the account after interest.
- $P$ is the initial principal (deposit).
- $r$ is the annual interest rate (in decimal form).
- $n$ is the number of times interest is compounded per year.
- $t$ is the time in years.

### Step 1: Express the Known Values
- The current amount $A = 4000$ (after 15 years).
- The annual percentage rate (APR) $r = 4.6\%$, or $r = 0.046$.
- The compounding is monthly, so $n = 12$.
- The time $t = 15$ years.

We will first calculate the initial deposit $P$ by rearranging the formula to solve for $P$.

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

### Step 2: Calculate the Initial Deposit

Once we find $P$, we'll calculate the amount that was in the account 4 years ago. This means we'll use $t = 11$ years (since 4 years ago is 11 years after the deposit was made). Let me compute this.The amount in your bank account 4 years ago was \$3328.91.

Would you like further details or have any questions? Here are 5 related questions to deepen your understanding:

1. How does the compounding frequency affect the final amount in an account?
2. What would the balance be if the interest compounded yearly instead of monthly?
3. How much interest did you earn over the past 4 years?
4. What is the difference between simple and compound interest?
5. How would the result change if the APR was 5% instead of 4.6%?

**Tip:** The more frequently interest is compounded, the greater the accumulated amount, because interest is earned on the previously earned interest more often.

Suppose that my bank account compounds monthly at an APR of 4.6%. If I haven’t touched the account since I made my initial deposit 15 years ago, how much money was in my account 4 years ago if my current balance is $4000? (round down to 2 decimal places)

Learn how to calculate the amount of money in a bank account using the compound interest formula with monthly compounding at a 4.6% APR. This example walks through a step-by-step solution to find the balance from 15 years ago and determine how much money was in the account 4 years ago. Suitable for high school students.

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