The formula for the monthly payment required to pay off a loan with a set rate o

Question

The formula for the monthly payment required to pay off a loan with a set rate of interest by the end of a specified amount of time can be thought of as a multivariable function. Let A = f(P, r, t) where A is the amount of the required monthly payment when P represents the principal amount borrowed r represents the interest rate, and t represents the length of the loan term. (a) Do you expect the sign of f_p be a positive or negative? Explain. (b) Do you expect the sign of f_r be a positive or negative? Explain. (c) Do you expect the sign of f_t be a positive or negative? Explain.

Explanation / Answer

a) Positive

The monthly installment of the loan will obviously increase if we increase the principal loan amount assuming the rate and time period to remain same. So, the rate of change of installment amount with respect to principal amount would be positive.

------------------------

b) Positive

Again, the monthlyinstallment amound would obviously increase if you increase the rate percentage keeping the principal loan amount and the time period of the loan constant. So, rate of change of installment amount with respect to rate would be positive.

-----------------------------------

c) Negative

Now, if you keep the loan principal amount and the rate constant and then pay the same loan over a longer period of time, you obviously will have to pay a less installment each period. So, the rate of change would be negative in this case.

__________________________________

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.