Question

Describe the effect an increase in i, the interest rate applied to the present value, has on the monthly payment P in the formula
P = P V times StartFraction i over 1 minus (1 + i) superscript negative n Baseline EndFraction
a.
An increase in i, the interest rate, will not change P, the monthly payment.
b.
An increase in i, the interest rate, will create an increase in P, the monthly payment.
c.
An increase in i, the interest rate, will create a decrease in P, the monthly payment.
d.
An increase in i, the interest rate, can increase or decrease P, the monthly payment, depending on the value of PV.

Answer 1

Answer: b.

Reason: P = PV * f(i) where f(i) = i / (1 - (1+i)^{-n}). One can show f'(i) > 0 for i > 0 (so f is increasing), hence P increases when i increases. Intuitively, a higher interest rate raises the interest portion of each installment, so the fixed-term payment must increase.