To determine how much you need to deposit today in order to accumulate $84,000 in 8 years with an interest rate of 0.51% per month, we can use the present value formula for compound interest.

The formula is:

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

Where:

• $PV$ is the present value (the amount to deposit today)
• $FV$ is the future value ($84,000)
• $r$ is the monthly interest rate (0.51% or 0.0051)
• $n$ is the total number of periods (8 years * 12 months/year = 96 months)

Step 1: Plug in the values

$PV = \frac{84,000}{(1 + 0.0051)^{96}}$

Step 2: Calculate the denominator

$1 + 0.0051 = 1.0051$

$1.0051^{96} \approx 1.647$

Step 3: Calculate the present value

$PV = \frac{84,000}{1.647} \approx 50,998.44$

So, you would need to deposit approximately $50,998.44 today in order to have $84,000 in 8 years with a monthly interest rate of 0.51%.

Would you like further clarification or have any additional questions on this? Here's some related content:

1. How does the compound interest formula change with different compounding frequencies?
2. What is the impact of a higher interest rate on the present value?
3. How does time affect the amount you need to deposit today in compound interest?
4. What happens if you deposit monthly instead of a lump sum today?
5. How can you calculate the future value of regular monthly deposits?

Tip: When working with compound interest, always ensure that the interest rate and time period are in the same units (e.g., monthly rate and months).