To solve this question, we need to carefully understand the components and variables in the given loan payment formula:
[tex]\[
P = PV \cdot \frac{i}{1 - (1 + i)^{-n}}
\][/tex]
Where:
- \(P\) is the monthly payment.
- \(PV\) is the present value or the loan amount.
- \(i\) is the interest rate per period.
- \(n\) is the number of periods.
Let's break down what each variable represents:
- \(P\): The monthly payment you need to make to repay the loan.
- \(PV\): The initial loan amount or present value.
- \(i\): The interest rate per period (monthly in this case since it's used to calculate the monthly payment).
- \(n\): The number of periods over which the loan is repaid.
Given the options:
a. number of periods over which interest is calculated on the loan
b. number of applicants for the loan
c. number of years it will take to pay the loan back
d. number of dollars the loan is for
Option a: This directly relates to the number of periods or time intervals (like months) over which the interest is calculated and the loan is to be repaid. This fits our interpretation of \(n\).
Option b: The number of applicants for the loan does not appear in the formula and is not relevant to \(n\).
Option c: The number of years it will take to pay the loan back could be a possible interpretation if the periods \(n\) are in years. However, typically, \(n\) is the total number of periods (months), not specifically years. Hence, this option does not fit well.
Option d: The number of dollars the loan is for corresponds to \(PV\), the present value, not \(n\).
After evaluating the options, the best answer is:
a. number of periods over which interest is calculated on the loan
