To determine how much the client needs to invest now to purchase an annuity that pays $100,000 each year for 6 years, starting 7 years from now, we need to follow these steps:

Step 1: Calculate the Present Value of the Annuity

First, calculate the present value (PV) of the annuity payments at the time when the first payment is made, which is 7 years from now.

The formula for the present value of an annuity is:

$PV = P \times \frac{1 - (1 + r)^{-n}}{r}$

Where:

• $P$ is the annuity payment ($100,000).
• $r$ is the interest rate (7% or 0.07).
• $n$ is the number of payments (6 years).

$PV = 100,000 \times \frac{1 - (1 + 0.07)^{-6}}{0.07}$

Step 2: Discount the Present Value Back to Today

Next, discount this PV back to the present time (0 years). This step accounts for the 7-year period before the first payment is made.

The formula to discount the present value back to today is:

$PV_{\text{today}} = PV_{\text{annuity}} \times \frac{1}{(1 + r)^t}$

Where:

• $t$ is the number of years until the first payment (7 years).

Let's calculate this.The client would need to invest $296,836.13 today to purchase an annuity that pays $100,000 each year for 6 years, with the first payment 7 years from now, assuming a 7% interest rate.

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

Here are 5 related questions:

1. How does the interest rate affect the present value of the annuity?
2. What would happen if the first payment were to be made immediately instead of after 7 years?
3. How would a change in the number of years of payment (e.g., from 6 to 8 years) impact the investment amount?
4. What if the payments were made semi-annually instead of annually?
5. How would an increase in the interest rate to 8% affect the initial investment?

Tip: Understanding how to discount future cash flows is essential for evaluating long-term investments like annuities.