To obtain the full credit, you must show the work that leads to the answer. 1. W

Question

To obtain the full credit, you must show the work that leads to the answer. 1. What simple interest rate per year would be required to accumulate the same amount of money in 2 years as 20% per year compound interest? (10 points) (a) 10.5% (b) 11% (c) 20% (d) 22% (e) 23% 2, Mary purchases a bond having a face value of $1,000 for $950. The bond rate is 8% payable semi-annually. The bond has a remaining life of 5 years. Assume the bond will be redeemed for face value. The yield rate earned on the investment is nearest to? (a) Less than 4% (b) equal to 4% (c) more than 4% and less than 8% (d) equal to 8% (e) greater than 8% (10 points)

Explanation / Answer

1. Let, the principle = P

Rate of interest per year, r = 20? = 0.2

Time period (in years) = t = 2

Therefore, with a compound interest rate of 20? per year after 2 years, Amount (A) = P ( 1+ r)t = P(1+ 0.2)2 = 1.44 P

Compound interest = A - P = 1.44P - P = 0.44 P

With a simple interest, if principle = P , rate of interest per year = r , Time period = t and total simple interest = 0.44 P ( as it is given in the question that same amount of money would be acquired as it is obtained after 2 years with a 20? per year compounded interest) :

Therefore, simple interest = P * r * t

Or, 0.44P = Prt

Or, r * 2 = 0.44

Or, r = 0.44/2 = 0.22

Therefore, simple interest per year = r = 0.22 = 22?

Answer- option D

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