To determine how much to deposit now in order to have $3,000 in the account in 10 years, we need to use the formula for the present value (PV) of a future sum when compounded interest is involved:

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

Where:

• $PV$ = present value (the amount we need to deposit now)
• $FV$ = future value ($3,000)
• $r$ = annual interest rate (0.07 for 7%)
• $n$ = number of times the interest is compounded per year (4 for quarterly)
• $t$ = time in years (10 years)

Step-by-Step Calculation

1. Identify the variables:

   • $FV = 3000$
   • $r = 0.07$
   • $n = 4$
   • $t = 10$

2. Calculate the compounded factor: $(1 + \frac{0.07}{4})^{4 \times 10} = (1 + 0.0175)^{40}$

3. Compute the present value: $PV = \frac{3000}{(1.0175)^{40}}$

Let's compute this.To have $3,000 in the account after 10 years with a 7% interest rate compounded quarterly, you would need to deposit approximately $1,498.80 now.

Would you like a detailed breakdown of the calculations or have any further questions?

Here are 5 related questions you might find interesting:

1. How would the required initial deposit change if the interest rate was 5% instead?
2. What if the compounding frequency was monthly instead of quarterly?
3. How much total interest would you earn over the 10 years?
4. How long would it take for an initial deposit of $1,500 to grow to $3,000 at a 7% interest rate compounded quarterly?
5. What is the future value if you deposit $1,500 at 7% interest compounded annually?

Tip: The more frequently interest is compounded, the greater the amount of interest accrued over time due to the effects of compounding.