In r denotes a yearly interest rate expressed as a decimal (rather than as a percent). If P dollars are deposited every month in an account earning interest at the yearly rate r, then the value S of the account after N years is

You have decided to deposit P = $100 per month.

(a) Determine S after 5 years if r = 0.07 (i.e., 7%).
(b) Show that to save $10,000 after 5 years, you must earn interest at a rate r determined by the equation b⁶¹ − 101b + 100 = 0. Use Newton’s Method to solve for b. Then find r. Note that b = 1 is a root, but you want the root satisfying b > 1.

Transcribed Image Text:

S = P 12N+1 - b ;). b-1 where b = 1 + r 12