A $500,000 loan can be amortized over 15 years with annual payments of $58,414.77 at j₁ = 8% (option A).Alternatively,$500,000 can be borrowed at j₁ = x%,with interest paid at the end of each year and the principal repaid with one lump sum at the end of 15 years (option B).For option B,a sinking fund can be set up earning j₁ = 6%.What is the value of x% such that the annual expense under the two options is the same?

Question

Quizplus · Accepted Answer

The correct answer is A because the annual expense under option A is $58,414.77, and the annual expense under option B is $500,000 * x% + $500,000 / (1 + 0.06)^15 = $58,414.77. Solving for x%, we get x% = 7.39%.

A $500,000 Loan Can Be Amortized Over 15 Years with Annual