The situation described in this question is different in that the evaluation per

Question

The situation described in this question is different in that the evaluation period is from when Mr. Gonzalez purchased the bond 4 years ago to today, when he is considering selling the bond. Here are some notes to help you understand the situation and what is being asked.

a) Four years ago Mr. Gonzalez purchased the bond from someone else for $920.

b) The bond pays interest at the rate of 8% per year with payments semi-annually.

c) Mr. Gonzalez wishes to have earned at least 9% per year compounded semi-annually over the 4 years that he will have owned the bond.

d) He is selling the bond to someone else

Explanation / Answer

Step1. First we have to calculate effective Annual Rate of 8% interest that bond pay semi annualy return if Compounded Half Yearly.

Formula to Calculate: i = (1 + r/m)m - 1

i = Effective annual Interest Rate required, r = Actual Rate of Interest, m = Number of Compounding Per Year

Given, i = ?, r = 8% , m = 2

By putting Value: i = (1+ 8 / 2)2 - 1

By solving equation we get, i = 8.16%

Required Annual Return if compounded semi annually = 9%

Formula to Calculate semi annual rate: i = (1 + r/m)m - 1

i = Effective annual Interest Rate required, r = Actual Rate of Interest, m = Number of Compounding Per Year

Given, i = 9%, r = ?, m = 2

By putting Value: 9 = (1+ r / 2)2 - 1

By solving equation we get, i = 8.80%

So, the difference is 8.80 - 8.16 = 0.64%

The Minimum Price should be:

Calculation of minimum Price by applying Compound Interest Formula:

FV = P (1+ r/n) nt

FV = Future Value, P = Price, r = Rate of Interest, t = Number of Years, n = Compounding Frequency

P = 920, r = 0.64, t = 4 Years, n =2

By Putting Value:

FV = 920 (1+ 0.00639 / 2)2x4

FV = $943.78

So, the minimum selling Price should be = $943.81

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