SOLUTION: I purchased 100 shares of stock for $23.75 per share. Eight months later I sold the stock at $24.50 per share. (a.)What annual rate, using simple interest did I earn on this trans

Question 962493: I purchased 100 shares of stock for $23.75 per share. Eight months later I sold the stock at $24.50 per share.
(a.)What annual rate, using simple interest did I earn on this transaction?
(b.) What annual rate would I have to earn in a saving account compounded monthly to earn the same money on my investment?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Profit for 1 share: $24.50 - $23.75 = $0.75

Profit for 100 shares: 100*($0.75) = $75

So effectively, you have earned $75 in interest. The initial principal is 100*($23.75) = $2375

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a)

I = P*r*t

75 = 2375*r*(8/12) ... note: t is in years, 8/12 years = 8 months

75 = 1,583.3333*r

r = 75/1,583.3333

r = 0.04736

r = 4.74%

The interest rate is roughly 4.74%
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b)

A = P*(1+r/n)^(n*t)

P + I = P*(1+r/n)^(n*t)

2375+75 = 2375*(1+r/12)^(12*8/12)

2450 = 2375*(1+r/12)^8

2450/2375 = (1+r/12)^8

1.0315789 = (1+r/12)^8

1+r/12 = 1.0315789^(1/8)

1+r/12 = 1.00389

r/12 = 1.00389 - 1

r/12 = 0.00389

r = 12*0.00389

r = 0.04668

r = 4.67%

The interest rate needed is approximately 4.67%

If you need more one-on-one help, or if you have any questions, email me at jim_thompson5910@hotmail.com

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