Sally wishes to purchase a stereo system. She is offered the following payment o
ID: 408638 • Letter: S
Question
Sally wishes to purchase a stereo system. She is offered the following payment options: Determine the range of interest rates for which the present value of Option 1 is less than the present value of Option 2. Use Level 2 CES EduPack to answer the EduPack-based questions, Identify materials on the graphs by using the label function available in EduPack. Draw a bubble chart in Metric units showing tensile strength on X-axis and hardness (HV) on Y-axis. How do the hardness of ceramics, metals and polymers compare? Do you see any correlation between tensile strength and hardness? If yes, describe it in words.Explanation / Answer
The present value of 'P1' in 1 year at rate of interest 'r' is P1/(1+r) and present value of P2 in 2years is P2/(1+r)2
Present value of option 1 is 432/(1+r) + 300/(1+r)2
Present value of option 2 is 82.56 + 250/(1+r) + 400/(1+r)2
As per the question we are required to find range of 'r' so that
432/(1+r) + 300/(1+r)2 < 82.56 + 250/(1+r) + 400/(1+r)2
or 432(1+r) + 300 < 82.56(1+r)2 + 250(1+r) + 400
On solving the above equation the roots of quadratic equation of (1+r) gives roots as 1.16279 and 1.04166
Therefore we can conclude that if rate of interest is less than 4.166% or rate of interest is more than 16.279% the present value of option 1 will be less than the present value of option 2.
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