Investment word problem?

Question

On December 31, 1995, Paul invested $2,000 in a stock. Since then, his stock has gained 20% in every odd-numbered month (January March, and so on) but lost 15% in every even-numbered month (February, April, and so on)

(a) Find the value of the stock at the end of each of the first five months in 1996.

(b) Write a piecewise defined function f(n) for the value of the stock n months after the ooriginalinvestment, where n is a whole number.

(c) Name the first time when the value of the stock at the end of the month is at least twice the original investment.

Any help is much appreicated. Please show work so i can solve similar problems. Thanks and 10 points to a best answer

Answer 1

(a)

2000 * 1.2 * 0.85 * 1.2 * 0.85 * 1.2 = 2496.96

(b)

f(n) = 2000 * 1.02^(n/2) [even n]

f(n) = 2400 * 1.02^((n-1)/2) [odd n]

(c)

lose money in even months, so solve for first odd month

4000 = 2400 * 1.02^((n-1)/2)

5/3 = 1.02^((n-1)/2)

n= 2 * log(5/3)/log(1.02)+1

n = 52.6

first month is 53