finding interest

Question

Willard Husdon took out a simple interest loan of $6000.00 at 10% interest for 24 months. His monthl payment is $276.60. After 4 payments the balance is $5,082.21. He pays off the loan when the next payment is due. What is the interest? What is the final payment? How much is saved by paying the loan off early?

Answer 1

Aside from a minor error in calculating the monthly payment A, for a loan of B₀, and monthly interest rate of r, for a number of months N

A=B₀r/(1-1/(1+r)^N)= in our case (6000×.1/12)/(1-1/(1+.1/12)²⁴) = 276.869558

The balance after the k^th payment, B_k = B₀(1+r)^k - (A/r)×((1+r)^k-1)

B₄ = 5081.1154.  If he pays off the loan at the time when the fifth payment is due, the interest is

rB₄ =5081.1154× .1/12 = 44.28086527

The total final payment in this case is 5123.4577.

The mount of interest in this case is r(B₀+B₁+B₂+B₃+B₄)=230.9359976

The total interest for the 24 month loan would be 644.8693926

The savings for early payment is 413.933395