a) A payday loan company is willing to lend you $1,000.00, however, you must pay

Question

a) A payday loan company is willing to lend you $1,000.00, however, you must pay them back $1,080.00 by the end of the week. You can assume 52 weeks in a year. i.) (4 pts) What is the nominal interest rate (inom)? i.) (4 pts) What is the effective annual interest rate (ie)? b) 8 pts) You bought 100 shares of Cisco stock for $2,243 on December 31, 2013. Your intention is to keep the stock until it doubles in value. If you expect 12% annual growth for the Cisco stock, how many years do you expect to hold onto the stock before selling? c) (8 pts) The accompanying diagram shows the anticipated cash dividends for GoGoMa Inc. over the next four years. Kelly is interested in buying some shares of this stock for a total of $100 now and will hold them for four years. If Kelly's interest rate is 8% compounded annually, what would the desired (minimum) total selling price (X) for the set of shares be at the end of the fourth year? X-? 0 2 4 P- $100

Explanation / Answer

(a)

(i) Nominal interest rate = ($1,080 / $1,000) - 1 = 1.08 - 1 = 0.08 = 8%

(ii) Effective annual interest rate = [1 + (0.08 / 52)]52 - 1 = [1 + (0.0015)]52 - 1 = [1.0015]52 - 1 = 1.0832 - 1 = 0.0832

= 8.2%

(b)

Let the number of years to double be N. Then,

$2,243 x (1.12)N = 2 x $2,243

(1.12)N = 2

Taking natural logarithm on each side,

N x ln 1.12 = ln 2

N x 0.1133 = 0.6931

N = 0.6931 / 0.1133

N = 6.12 years

NOTE: First 2 questions are answered.

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