233 Example 2.3.6-1

An annuity immediate pays 15 at the end of years 1 and 2, 14 at the end of years 3 and 4 and so on.

The payments decrease by 1 every second year until nothing is paid.

The effective annual interest rate is 6%.

Calculate the present value of this annuity. (use a decimal number, rounded to the nearest 100th. For example, 123.45)

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233 Example 2.3.7-1

Francois purchases a 10-year annuity-immediate with annual payments of 10X. Jacques purchases a 10-year decreasing annuity-immediate which also makes annual payments. The payment at the end of year 1 is equal to 50. At the end of year 2, and at the end of each year through year 10, each subsequent payment is reduced over what was paid in the previous year by an amount equal to X. At an annual effective interest rate of 7.072%, both annuities have the same present value. Calculate X, where X < 5.