How much would a business have to invest in a high-growth fund to receive $25,000 every month for 5 years, receiving the first payment 2 years from now? The investment earns interest at 6.50% compounded monthly.

To determine the amount of investment required to receive $25,000 every month for 5 years, with the first payment starting 2 years from now and an interest rate of 6.50% compounded monthly, we can break the problem into two parts:

1. Calculate the present value (PV) of the annuity (monthly payments).
2. Determine the initial investment needed to accumulate this present value in 2 years.

### Step 1: Present Value of the Annuity

Given:
- Monthly payment ($ PMT $) = $25,000
- Number of payments ($ n $) = 5 years × 12 months/year = 60 payments
- Monthly interest rate ($ i $) = 6.50% / 12 months = 0.54167% = 0.0054167

The present value of an annuity formula is:

\[ PV = PMT \times \frac{1 - (1 + i)^{-n}}{i} \]

Substituting the values:

\[ PV = 25,000 \times \frac{1 - (1 + 0.0054167)^{-60}}{0.0054167} \]

Calculating the present value:

\[ PV = 25,000 \times \frac{1 - (1.0054167)^{-60}}{0.0054167} \]
\[ PV = 25,000 \times \frac{1 - 0.741425}{0.0054167} \]
\[ PV = 25,000 \times \frac{0.258575}{0.0054167} \]
\[ PV = 25,000 \times 47.748 \]
\[ PV = 1,193,700 \]

### Step 2: Initial Investment to Accumulate the Present Value

The PV calculated above is the amount needed 2 years from now. To find the initial investment, we discount this amount back over the 2 years using the compound interest formula.

Given:
- Future value ($ FV $) = $1,193,700
- Interest rate ($ i $) = 6.50% / 12 = 0.54167% = 0.0054167
- Number of periods ($ n $) = 2 years × 12 months/year = 24 periods

The formula to find the present value ($ PV $) is:

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

Substituting the values:

\[ PV = \frac{1,193,700}{(1 + 0.0054167)^{24}} \]

Calculating:

\[ PV = \frac{1,193,700}{(1.0054167)^{24}} \]
\[ PV = \frac{1,193,700}{1.138608} \]
\[ PV = 1,048,310.23 \]

### Conclusion

The business would need to invest approximately $1,048,310.23 today in the high-growth fund to receive $25,000 every month for 5 years, with the first payment starting 2 years from now.

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

Here are 5 numbered questions you might ask next:
1. Can you explain how the present value of an annuity is calculated?
2. How does compound interest affect the initial investment calculation?
3. What if the interest rate was different? How would that change the investment needed?
4. Can you show the formula derivations for these calculations?
5. How would the calculation change if the payments were to start immediately instead of 2 years from now?

**Tip:** Always ensure to adjust the interest rate and time period appropriately when calculating present values or future values in finance problems.

Learn how to calculate the initial investment required to receive $25,000 monthly payments for 5 years, starting 2 years from now. Includes step-by-step solution using finance formulas and compound interest calculations.

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