A $200,000 debt at j₂ = 7% is being repaid over 10 years using the sinking fund method,where the sinking fund earns interest at j₂ = 6%.What is the book value of the loan at the end of 6 years?

Question

Quizplus · Accepted Answer

Using the sinking fund method, we need to calculate the periodic payment to the sinking fund and the book value of the loan at the end of 6 years.

Periodic Payment to Sinking Fund:
PV = FV/(1+i)^n
PV = 200,000/(1+0.06)^10 = 104,040.30
PMT = PV/( (1+i)^n -1) * i
PMT = 104,040.30/ ((1+0.06)^10 -1) * 0.06
PMT = 19,634.05

Book Value of Loan at the End of 6 Years:
PV = PMT /(1+i)^n-1 * (1-1/(1+i)^n)
PV = 19,634.05/(1+0.06)^6-1 * (1-1/(1+0.06)^6)
PV = 94,366.72

Therefore, the book value of the loan at the end of 6 years is $94,366.72 (Option C).

A $200,000 Debt at J2 = 7% Is Being Repaid

A $200,000 Debt at J₂ = 7% Is Being Repaid