\"You are borrowing $2,600 now, which you will pay back at the end of 15 years.

Question

"You are borrowing $2,600 now, which you will pay back at the end of 15 years. You are considering two separate interest rates: a. A fixed 7.8% annual interest rate. b. A variable interest of 4.8% annual interest for the first 5 years; 8.5% 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 15 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 15 years. Enter your answer as a percentage between 0 and 100."

Explanation / Answer

Total amount that would be paid = 2600*1.048^5*1.085^5*(1+i)^5

Solution: Under Option A: Fixed Interest rate @7.8% Total amount that would be paid = $2600*1.078^15 = $8021.4847 Under Option B: Variable Interest Rate

Total amount that would be paid = 2600*1.048^5*1.085^5*(1+i)^5

Equation the two, we have 8021.4847=2600*1.048^5*1.085^5*(1+i)^5 Solving for i 8021.4847/(2600*1.048^5*1.085^5) = (1+i)^5 1.623029 = (1+i)^5 i = 1.623029^(1/5)-1 = 10.17% One is indifferent at i = 10.17% [Answer]

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