Question

Describe the effect an increase in n, the number of payment periods, 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 n, the number of payment periods, will not change P, the monthly payment.
b.
An increase in n, the number of payment periods, will create an increase in P, the monthly payment.
c.
An increase in n, the number of payment periods, will create a decrease in P, the monthly payment.
d.
An increase in n, the number of payment periods, can increase or decrease P, the monthly payment, depending on the value of PV.

Answer 1

c.

Reason: For i > 0, (1 + i)^(−n) decreases as n increases, so 1 − (1 + i)^(−n) increases. That makes the fraction i / [1 − (1 + i)^(−n)] smaller, so P = PV × that fraction decreases. (If i = 0 the formula reduces to P = PV/n, which also decreases as n increases.)