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County Ranch Insurance Company wants to offer a guaranteed annuity in units of $500, payable at the end of each year for twenty-five years. The company has a strong investment record and can consistently earn 7% on its investments after taxes. If the company wants to make 1% on this contract, what price should it set on it? Use 6% as the discount rate. Assume it is an ordinary annuity and the price is the same as present value.

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TomShelby

Answer:

It will price the annuity service at 6,391.68 dollars

Explanation:

The company will earn at 7% from the amount charged at the customer. To make 1% it will discount at 6% (7% - 1%) This will make the present value of the annuity lower that if earned at 7% This difference is the gain for County Ranch.

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]  

C $500

time 25 years

rate 0.06

[tex]500 \times \frac{1-(1+0.06)^{-25} }{0.06} = PV\\[/tex]  

PV $6,391.6781  

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