Let Qn and In be as defined in Exercise 37.
Refer in Exercise 37,
Let Bn = balance of a loan after n payments, In = the interest portion of the nth payment, and Qn = the portion of the nth payment applied to the principal. Equation (1) states that Bn = (1 + i)Bn-1 - R.
(a) Use the result in part (b) of Exercise 37 and the facts that Qn+1 = R - In+1 and Qn = R - In to show that In+1 = (1 + i)In - iR.
(b) State in your own words the formula obtained in part (a).
(c) Suppose that, for a loan with a monthly payment of $400 and an interest rate of 1% per month, $100 of the 9th monthly payment goes toward paying off interest. How much of the 10th and 11th payments will be used to pay off interest?