The Smiths want to buy life insurance for Chris, who earns $115,000/year. They w

Question

The Smiths want to buy life insurance for Chris, who earns $115,000/year. They want an insurance amount sufficient, if invested in an annuity, to cover 100% of Chris's annual nominal income for 10 years and 75% of that annual nominal income for an additional 10 years. They anticipate a 5% yield rate on the annuity as well as on saved funds. Assume all payments occur at year end. How much insurance should they buy? [Hint: Compute more than one annuity value then figure out how to combine them. Chose the interval that contains your calculated answer.]

Explanation / Answer

I missed a detail of the problem ("payments at end of year"). The revised calculation is $1,296,865.50. I solved this by spreadsheet. Each year's balance is calculated as (Last year's money * 1.05 - 115,000) for the first 10 years, then (Last year's money * 1.05 - 86,250) for the next 10 years. Pick an initial value so that you run down to $0 at the end of 20 years. I played around with different numbers, until I got closer and closer. I don't think that there's a simple formula for calculating the value of a finite-duration annuity; you need to program it out in Excel or something like that.

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