a) Show that the discounted value A of a decreasing annuity whose n payments at the end of each year are nR, (n 1)R, (n 2)R,...., 2R, R is:

A = (R/i) (n a_(n)i) at rate i per year.

b) Let us assume that A = 3955$, R = 300$ and n = 5. Use linear interpolation to determine the interest rate i, rounded to two decimals, between 5% and 6%. Show if the price A of this annuity at your estimated interest rate is within a range of 10$ of 3955$.