To determine the amount you need to deposit now, you can use the present value formula for compound interest:

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

Where:

• $PV$ = Present Value (initial deposit)
• $FV$ = Future Value ($5000)
• $r$ = Annual interest rate (0.02 or 2%)
• $n$ = Number of compounding periods per year (12 for monthly compounding)
• $t$ = Time in years (15)

Plugging in the values:

$PV = \frac{5000}{(1 + \frac{0.02}{12})^{12 \cdot 15}}$

Simplify:

1. $\frac{0.02}{12} = 0.0016667$
2. $12 \cdot 15 = 180$
3. $1 + 0.0016667 = 1.0016667$
4. $(1.0016667)^{180} \approx 1.34935355$
5. $PV = \frac{5000}{1.34935355}$

$PV \approx 3705.41$

Final Answer:

You need to deposit approximately $3705.41 now to have $5000 in 15 years at 2% interest compounded monthly.

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Would you like further explanation or a breakdown of the steps? Here are 5 follow-up questions to deepen your understanding:

1. How does the frequency of compounding affect the amount you need to deposit?
2. What would the required deposit be if the interest rate were higher (e.g., 3%)?
3. How would the calculation change if the interest were compounded annually instead of monthly?
4. What is the total interest earned over the 15 years in this scenario?
5. How can this formula be used to plan for larger financial goals?

Tip: Compounding more frequently leads to slightly higher future values for the same interest rate and time period!