In repaying a loan of amount L, the total periodic outlay made by a borrower at time t is K_t for t = 1, 2, .. ., n. The borrower pays interest on L at rate i, with the rest of the outlay going into a sinking fund earning rate j to accumulate to L at time n. Solve for L in terms of i, j, n, and the K_t's. Let X be the present value of the K_t's at rate j per period. Show that L can be written in the form X/Y, and solve for Y. Show that Y = 1 if i = j .