Your grandmother bought an annuity from Rock Solid Life Insurance Company for $200,000 when she retired. In exchange for the $200,000, Rock Solid will pay her $25,000 per year until she dies. The interest rate is 5%. How long must she live after the day she retired to come out ahead (that is, to get more in value than what she paid in)

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lisandroprieri lisandroprieri · Answer 1 · 2019-09-11T18:55:28+02:00

Answer:

The number of years she has to live to come out ahead is 11 (or 10.47 to be precise).

Explanation:

We know that she breaks even the the net present value (NPV) is 0. Having the following data:

- Initial value (IV) = -$200,000

- Final value (FV) = 0

- Interest rate (r) = 5% = 0.05

- Payment (P) = $25,000

The formula for the number of years she must live to come out ahead (n) is given by:

[tex]n = Log_{10}(P/(P+IV\div r))/Log_{10}(1+r)[/tex]

Replacing in the formula with the known values we have:

[tex]n = Log_{10}(25000/(25000-200000\div 0.05))/Log_{10}(1+0.05) = 10.4698 \approx 11[/tex]

Therefore the number of years grandma has to live to come out ahead is 11 (or 10.4698 to be more precise).