In installment buying, one would like to figure out the real interest rate (effective rate), but unfortunately this involves solving a complicated equation. If one buys an item worth $P today and agrees to pay for it with payments of $R at the end of each month for k months, then

Where i is the interest rate per month, Tom bought a used car for $2000 and agreed to pay for it with $100 payments at the end of each of the next 24 months.
a. Show that i satisfies the equation
20i(1 + i)24 -(1 + i)24 + 1 = 0
b. Show that Newton's Method for this equation reduces to

c. Find i accurate to five decimal places starting with i = 0.012, and then give the annual rate r as a percent (r = 1200i).

Transcribed Image Text:

20i; +191,-1+ (1 + in厂23 rI 500i,-4