Answer to Question #65289 in Financial Math for Stephanie Joyce Diaresco Yu

Question

A loan is to be amortized by semi-annual payments of $5,700 each with the interest at 15% compounded semi-annually. If the outstanding balance at the end of 6 years is $78,890.24.

A) Find the original amount borrowed.
B) How may regular semi-annual payments are needed?
C) What is the repayment of the principal in the 11th payment?

Answer 1

A loan is to be amortized by semi-annual payments of $5,700 each with the interest at 15% compounded semi­annually. If the outstanding balance at the end of 6 years is $78,890.24.

A) The original amount borrowed is:
(78,890.24 + 5,700*12)/(1 + 0.15/2)^12 = 61,840.42
B) The number of regular semi-annual payments needed is:
N = -log(1 - 0.15*5,700/61,840.42)/log(1.15) = 0.1.
C) The repayment of the principal in the 11th payment is $5,700.