A debt is amortized at j₄ = x%by payment of $300 per quarter.You are given that the outstanding balance is $6279.09 just after the k^th payment and the outstanding balance is $6136.07 just after the (k+1)^st payment.What is x?

Question

Quizplus · Accepted Answer

We can set up two equations to represent the outstanding balance after the kth payment and the (k+1)st payment:

6279.09 = 300[(1-(1+x/400)^-k)/(x/400)] 
6136.07 = 300[(1-(1+x/400)^-(k+1))/(x/400)]

Let's simplify these equations:

(1-(1+x/400)^-k)/(x/400) = 20.9303 
(1-(1+x/400)^-(k+1))/(x/400) = 20.4536

Dividing the first equation by the second, we get:

(1+x/400)^(k+1) = 1.02198

Taking the natural log of both sides:

(k+1) ln(1+x/400) = ln(1.02198)

Solving for x, we get x = 0.1 or 10%.

Therefore, the answer is B.

A Debt Is Amortized at J4 = X%by Payment of $300

A Debt Is Amortized at J₄ = X%by Payment of $300