You need $89,000 in 8 years. If you can earn .56 percent per month, how much will you have to deposit today?

To solve this problem, we can use the formula for the present value (PV) of a future sum, which is:

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

Where:
- $FV$ is the future value (\$89,000),
- $r$ is the monthly interest rate (0.56% = 0.0056),
- $n$ is the total number of periods (months), which is 8 years $\times$ 12 months/year = 96 months.

Now, let's calculate the present value:

\[
PV = \dfrac{89,000}{(1 + 0.0056)^{96}}
\]

I'll calculate that for you.You would need to deposit approximately **$52,067.24** today to reach $89,000 in 8 years at a monthly interest rate of 0.56%.

Would you like any additional details or clarifications?

Here are 5 related questions:
1. What is the future value if the interest rate changes to 0.6% per month?
2. How much interest would be earned in total over the 8 years?
3. What if you wanted $100,000 in 8 years instead of $89,000? How much should you deposit today?
4. How would the deposit change if the time period was 10 years instead of 8 years?
5. What if you made regular monthly deposits instead of a lump sum?

**Tip:** Small changes in the interest rate can significantly affect the amount you need to invest today, especially over long periods.

Find out how much you need to deposit today to reach $89,000 in 8 years with a monthly interest rate of 0.56%. This calculation uses the present value formula and compound interest principles, suitable for high school students or anyone learning about the time value of money.

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