How to Calculate the Annual Payment of Merlot in an Annuity Due Scenario

What is the concept of actuarial equivalence in the context of annuities?

How can we calculate the annual payment of Merlot, considering a whole life annuity due with the first 15 payments guaranteed?

Calculating the Annual Payment of Merlot

To calculate the annual payment of Merlot, we need to understand the concept of actuarial equivalence and apply it to the given scenario.

Actuarial equivalence means that two different financial arrangements have the same present value. Here, we are comparing the whole life annuity due of Cabernet with the whole life annuity due of Merlot, where the first 15 payments are guaranteed.

To calculate the annual payment of Merlot, we need to find the present value of both annuities and equate them. For Cabernet's annuity, we have an annual payment of $80,000. Using the present value of an annuity formula with mortality following the Standard Ultimate Life Table and i = 0.05, we can calculate the present value.

Now, for Merlot's annuity, considering the guaranteed 15 payments, we can discount these using the same formula as Cabernet's annuity. The remaining payments after the guaranteed period are similar to Cabernet's annuity.

To find the annual payment of Merlot, we equate the present values of both annuities. By comparing the present values of the options A, B, C, D, and E, we can deduce the correct annual payment amount for Merlot.

Without exact details of the annuities' length or the interest rate for the present value calculation, providing a definitive answer is not possible. However, you can calculate the present values for each option with the given information.