You are borrowing $3,600 now, which you will pay back at the end of 25 years. Yo
ID: 2784026 • Letter: Y
Question
You are borrowing $3,600 now, which you will pay back at the end of 25 years. You are considering two separate interest rates:
a. A fixed 8% annual interest rate.
b. A variable interest of 5.3% annual interest for the first 5 years; 5.7% annual interest rate for next 5 years; and i% interest rate for the remaining years. Assuming you desire to pay the least amount of money back at the end of 25 years, what value of i makes you indifferent between options a and b? With both options, you make exactly one payment at the end of 25 years. Enter your answer as a percentage between 0 and 100
Explanation / Answer
Total amount that would be paid under option [a] = 3600*1.08^25 = $ 24,654.51 Total amount that would be paid under option [b] = 3600*1.053^5*1.057^5*(1+i)^15 Equation the two, we have 24654.51=3600*1.053^5*1.057^5*(1+i)^15 Solving for i 24654.51/(3600*1.053^5*1.057^5) = (1+i)^15 4.009378732 = (1+i)^15 i = 4.009378732^(1/15)-1 = 9.70% One is indifferent at i = 9.70% [Answer]
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