The Mutual Assurance and Life Company is offering an insurance policy under either of the following two terms:

a. Make a series of 12 payments of 1,200 at the beginning of each of the next 12 years (the first payment being made today)

b. Make a single lump-sum payment today of 10,000 and receive coverage for the next 12 years

If you had investment opportunities offering an 8 percent annual return which alternative would you prefer?

a) is just the present value of an "annuity" and its value is

1200 + 1200[1 - 1.08^-11]/.08

b) is rather vague.
what is the coverage, is it $10,000?
What actuarial tables are used? (they are a factor of date, country, sex, etc)

If you are studying actuarial math, then there should be formulas for the present value of a term insurance in terms of Dx and Nx

To determine which alternative would be preferable, we need to compare the present values of the two options and see which one is higher.

Let's start with option a:

a. Make a series of 12 payments of 1,200 at the beginning of each of the next 12 years (the first payment being made today).

Since the payments are made at the beginning of each year, this is an annuity due. To calculate the present value of an annuity due, we can use the formula:

PV = PMT * [(1 - (1 + r)^-n) / r],

where PV is the present value, PMT is the payment made at the beginning of each period, r is the interest rate per period, and n is the number of periods.

In this case, PMT = $1,200, r = 8% = 0.08, and n = 12. Plugging these values into the formula:

PV_a = $1,200 * [(1 - (1 + 0.08)^-12) / 0.08]
PV_a ≈ $10,718.17

Now let's consider option b:

b. Make a single lump-sum payment today of $10,000 and receive coverage for the next 12 years.

Since this is a lump-sum payment made today, the present value is simply equal to the payment itself.

PV_b = $10,000

Comparing the present values of the two options, we see that PV_a ($10,718.17) is higher than PV_b ($10,000). This means that option a, making a series of 12 payments of $1,200 at the beginning of each of the next 12 years, would be preferable if you had investment opportunities offering an 8% annual return.