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The problem in the image is asking to determine the **Present Value (initial deposit)** of an investment, given the future value, interest rate, and compounding frequency.

Here are the details provided in the question:

- **Future Value** (FV): \$32,000
- **Interest Rate** (r): 6% per year, compounded daily
- **Time** (t): 7 years
- **Compounding Frequency**: Daily (assumed 365 days/year)

We can use the formula for **Present Value** (PV) with compound interest:

\[
PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}
\]

Where:
- $ PV $ = Present Value (initial deposit)
- $ FV $ = Future Value
- $ r $ = Annual interest rate (as a decimal, so 6% = 0.06)
- $ n $ = Number of times interest is compounded per year (365 for daily compounding)
- $ t $ = Number of years

### Plugging in the values:
- $ FV = 32,000 $
- $ r = 0.06 $
- $ n = 365 $
- $ t = 7 $

Let's calculate this.The initial deposit (Present Value) that Jada made 7 years ago, given the bank's 6% annual interest rate compounded daily, was approximately **$21,026.22**.

Would you like more details on any part of the solution, or do you have other questions?

Here are some related questions you may find helpful:
1. How would the initial deposit change with a different interest rate?
2. How does compounding frequency (monthly, quarterly, etc.) affect the Present Value?
3. What if the compounding were continuous? How would the formula differ?
4. Can you explain how compound interest grows faster than simple interest?
5. What happens if the investment duration is extended beyond 7 years?

**Tip**: When dealing with compound interest, more frequent compounding periods (like daily vs. monthly) result in slightly higher accumulated interest over time.

Jada deposited an amount of money in a bank 7 years ago. If the bank had been paying interest at the rate of 6%/year compounded daily (assume a 365-day year) and she has $32,000 on deposit today, what was her initial deposit?

Learn how to calculate the initial deposit given a future value of $32,000, a 6% annual interest rate compounded daily, and a 7-year time frame. Using the compound interest formula, find the Present Value (initial deposit) in this detailed step-by-step solution.

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