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)? Round the number of years to the nearest integer.
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:
n= Log10 (P/(p+IV/r))/Log10(1+r)
Replacing in the formula with the known values we have:
n= Log10 (25000/ (25000-200000/0.05)) / Log10(1+0.05) = 10.4698 or 11
Therefore the number of years grandma has to live to come out ahead is 11 (or 10.4698 to be more precise).
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