How much would you need to deposit in an account now in order to have $6000 in the account in 15 years? Assume the account earns 2% interest compounded monthly.

To determine how much you would need to deposit now to have $6000 in 15 years with 2% interest compounded monthly, we can use the formula for the present value of a future sum of money:

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

Where:
- $ PV $ is the present value (the amount you need to deposit now).
- $ FV $ is the future value (\$6000).
- $ r $ is the annual interest rate (2% or 0.02).
- $ n $ is the number of times the interest is compounded per year (12 for monthly compounding).
- $ t $ is the number of years (15 years).

Let's plug in the values and calculate:

\[
PV = \frac{6000}{\left(1 + \frac{0.02}{12}\right)^{12 \times 15}}
\]

First, calculate the monthly interest rate and the exponent:

\[
\frac{0.02}{12} = 0.0016667
\]

\[
12 \times 15 = 180
\]

Now, compute the value:

\[
PV = \frac{6000}{(1.0016667)^{180}}
\]

Finally, calculate the present value:

\[
PV \approx \frac{6000}{1.3498588} \approx 4444.92
\]

You would need to deposit approximately **$4,444.92** now to have $6000 in the account in 15 years with 2% interest compounded monthly.

Would you like more details on this calculation, or do you have any questions?

Here are some related questions:
1. How does the present value change with a higher interest rate?
2. What happens to the present value if the interest is compounded quarterly instead of monthly?
3. How much would you need to deposit if the interest rate was 3% instead of 2%?
4. How does continuous compounding affect the present value compared to monthly compounding?
5. What is the future value if you deposit $5000 now with the same interest rate and time period?

**Tip:** Compounding frequency significantly affects the present value. The more frequently interest is compounded, the less you need to deposit now to reach your desired future value.

Find out how much you need to deposit now to have $6000 in 15 years with 2% interest compounded monthly. This detailed explanation includes the compound interest formula and key calculations. Suitable for Grades 9-12.

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