You are the beneficiary of a life insurance policy. The insurance company informs you that you have two options for receiving the insurance proceeds. You can receive a lump sum of $50,000 today or receive payments of $641 a month for ten years. You can earn 6.5% on your money. Which option should you take and why

The $641 to be received monthly for ten years is the option to be taken.

The reason is that the present value (PV), i.e. today’s value, of $641 to be received monthly for ten years is $56,451.91 and this is greater than a lump sum of $50,000 to be received today.

Explanation:

In order to decide on which option to take, the present value (PV) of $641 to be received monthly for ten years has to be calculated. This is done using the present value (PV) of an ordinary annuity formula as follows:

PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (1)

Where;

PV = Present value of all the monthly amount to receive = ?

P = Monthly amount to receive = $641

r = Interest rate = 6.5% annually = (6.5% ÷ 12) monthly = 0.541667% monthly or 0.00541667 montlhly

n = number of period = 10 years = 10 × 12 months = 120 months

Substituting the values into equation (1), we have:

PV = 641 × [{1 - [1 ÷ (1 + 0.00541666666666667)]^120} ÷ 0.00541666666666667]

     = 641 × [{1 - [1 ÷ 1.00541666666666667]^120} ÷ 0.00541666666666667]

     = 641 × [{1 - [0.994612515540821]^120} ÷ 0.00541666666666667]

      = 641 × [{1 - 0.522962293183739} ÷ 0.00541666666666667]

      = 641 × [0.477037706816261 ÷ 0.00541666666666667]

      = 641 × 88.068499719925

PV = $56,451.91

The $641 to be received monthly for ten years is the option to be taken.

The reason is that the present value (PV), i.e. today’s value, of $641 to be received monthly for ten years is $56,451.91 and this is greater than a lump sum of $50,000 to be received today.

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