Math 230 finite

Question

Find the periodic payment R required to amortize a loan of P dollars over t years with interest charged at the rate of r%/year compounded m times a year. Round answer to the nearest cent.

Answer 1

When thinking about how a loan is amortized, it might help first to know the amount by which the amount owed grows as interest compounds. Assuming that the periodicity of payments is equal to the periodicity at which interest is compounded, then you can build the intuition for this by first computing the change in interest between periods: r / m. Then you take that amount and multiply it by the amount borrowed (A) to get the amount of interest per period (P) ==> P = A * (r / m). In other words, this is the amount that has to be paid each month just to keep the balance at the original amount. Next we have to realize that A needs to be paid over a specified period of time (t) and to extend the intuition about payments per period, the total number of payments that will occur is (t * m). If you take all of this, with a little math, you eventually arrive at:

P = A / {[(1 + (r / m)] ^ (t * m)} / {r * [(1 + r) ^ (n * m)]}