Question

describe the effect an increase in (n), the number of payment periods, has on the monthly payment (p) in the formula

\\p = pv \frac{i}{1 - (1 + i)^{-n}}\\

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).

Explanation:

Analyze the given formula

Using the Loan Monthly Payment knowledge point

$$ P = PV \frac{i}{1 - (1 + i)^{-n}} $$

where \(PV > 0\), \(i > 0\), and \(n > 0\).

Determine the effect of increasing \(n\)

Using the Loan Monthly Payment knowledge point

$$
LATEXBLOCK0
$$

Thus, an increase in \(n\) creates a decrease in \(P\).

Answer:

• 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. (Correct answer)
• d. An increase in \(n\), the number of payment periods, can increase or decrease \(P\), the monthly payment, depending on the value of \(PV\).