Chapter 10, Problem 76E

Linear relationship between $P$ and $M$ in the amortization formula. [In all the installment loans, assume that the term of the loan and the APR remain the same.]

a. Explain why, in the amortization formula, the monthly payment $M$ is proportional to the principal $P$. In other words, explain why if the monthly payment on a loan with principal $P$ is $M$, then the monthly payment on a loan with principal $cP$ (where $c$ is any positive constant) is $cM$. (Hint: What happens in the amortization formula when you replace $P$ by $cP$?)

b. Explain why if the monthly payment on a loan with principal $P$ is $M$, and the monthly payment on a second loan with principal $Q$ is $N$, then the monthly payment on a loan with principal $\left(P+Q\right)$ is $\left(M+N\right)$.