To solve this problem, we need to use the simple interest formula:

$A = P(1 + rt)$

where:

• $A$ is the future amount (total amount after interest),
• $P$ is the principal (initial amount deposited),
• $r$ is the interest rate per year (expressed as a decimal),
• $t$ is the time in years.

Given:

• $A = 815$ dollars (the total amount you want after 3 years),
• $r = 6\% = 0.06$,
• $t = 3$ years.

Our goal is to find $P$, the initial deposit.

Steps:

1. Substitute the known values into the formula: $815 = P(1 + 0.06 \times 3)$

2. Simplify inside the parentheses: $815 = P(1 + 0.18)$ $815 = P \times 1.18$

3. Solve for $P$: $P = \frac{815}{1.18}$

4. Calculate the result: $P \approx 690.68$

So, you would need to deposit approximately $690.68 to have $815 in 3 years at a 6% simple interest rate.

Would you like more details or have any other questions?

Here are some related questions for further understanding:

1. How would the required deposit change if the interest rate were higher, say 8%?
2. What if the interest were compounded annually instead of being simple interest?
3. How much total interest would you earn with this deposit over the 3 years?
4. What would happen to the deposit amount if you needed $1,000 instead of $815 in the same timeframe?
5. How does simple interest differ from compound interest over longer time periods?

Tip: Simple interest grows linearly with time, making it easier to calculate but often less profitable than compound interest over long periods.