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 c P (where c is any positive constant) is c M . ( Hint: What happens in the amortization formula when you replace P by c P ?) 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 ( P + Q ) is ( M + N ) .
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 c P (where c is any positive constant) is c M . ( Hint: What happens in the amortization formula when you replace P by c P ?) 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 ( P + Q ) is ( M + N ) .
Solution Summary: The author explains that the amortization formula monthly payment M is proportional to value P.
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
c
P
(where
c
is any positive constant) is
c
M
. (Hint: What happens in the amortization formula when you replace
P
by
c
P
?)
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
(
P
+
Q
)
is
(
M
+
N
)
.
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