To determine what [tex]\( i \)[/tex] represents in the given formula for calculating the monthly payment on a personal loan, we need to examine each part of the formula carefully. The formula provided is:
[tex]\[ P = PV \cdot \frac{i}{1 - (1 + i)^{-n}} \][/tex]
where:
- [tex]\( P \)[/tex] is the monthly payment.
- [tex]\( PV \)[/tex] is the present value or the loan amount.
- [tex]\( i \)[/tex] is the interest rate per period.
- [tex]\( n \)[/tex] is the total number of payment periods.
Let's break down the function of each variable:
- [tex]\( P \)[/tex] (monthly payment) represents the amount you will pay each month.
- [tex]\( PV \)[/tex] (present value) corresponds to the total loan amount.
- [tex]\( n \)[/tex] (number of payment periods) is the total number of monthly payments you will make across the life of the loan.
- [tex]\( i \)[/tex] is typically referred to as the periodic interest rate.
Since the payments are monthly, the interest rate [tex]\( i \)[/tex] must correspond to the interest rate for each period (monthly in this context). This means that the annual interest rate needs to be divided by 12 (assuming 12 payment periods in one year) to establish [tex]\( i \)[/tex].
From the given options:
a. annual interest rate
b. interest rate per period
c. initial amount
d. incident amount
The correct choice is:
b. interest rate per period
Thus, [tex]\( i \)[/tex] represents the interest rate per period in the loan calculation formula.
