To solve for the lump sum needed to fund the deferred annuity, we'll use the concept of the present value of an annuity.

Key Information:

• Monthly payment (PMT): $2000
• Number of payments (n): 5 years × 12 months = 60 payments
• Annual interest rate (r): 6% (compounded monthly, so $\frac{6\%}{12} = 0.5\%$ monthly interest rate)
• Interest rate per period (i): 0.005 (monthly interest rate)
• Deferred period: 2 years (24 months)
• Formula to use: The present value of an annuity due formula and the concept of deferral.

Solution Steps:

1. Present value of the annuity: The formula for the present value of an annuity is:

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

   where:

   • $PMT = 2000$ is the monthly payment,
   • $i = 0.005$ is the monthly interest rate,
   • $n = 60$ is the total number of payments (5 years × 12 months).

2. Deferral period: Since the annuity is deferred for 2 years, we need to calculate the present value of the annuity at the start of the 5-year period, then discount that value back 2 years to the present.

3. Discount the present value back by the deferral period: Once the present value of the annuity at the start of the 5-year period is calculated, it must be discounted for the 2-year deferral.

Let me calculate it for you.The lump sum that you need to invest now to fund the deferred annuity is approximately $91,780.35.

Would you like a more detailed breakdown or have any questions?

Here are 5 related questions to deepen your understanding:

1. How does the interest rate affect the present value of an annuity?
2. What would happen if the deferral period was extended to 3 years?
3. How is the formula for the present value of an annuity derived?
4. What would be the lump sum if the interest rate were 8% instead of 6%?
5. How can the monthly payment amount be adjusted to match a different lump sum?

Tip: When working with deferred annuities, always account for the deferral period by discounting the present value accordingly.