The following formula is used to calculate the monthly payment on a personal loan
[tex]$P=P V \cdot \frac{i}{1-(1+i)^{-n}}$[/tex]
In this formula, [tex]$i$[/tex] represents the ______ of the loan.
A. annual interest rate
B. interest rate per period
C. initial amount
D. incident amount
Answer (1)
The formula calculates the monthly payment on a loan.
Analyze the term ( 1 + i ) − 4 to understand the meaning of i .
Relate the formula to the concept of monthly payments.
Conclude that i represents the interest rate per period. The answer is B .
Explanation
Understanding the Formula The problem provides a formula for calculating the monthly payment on a personal loan: P = P V "." 1 − ( 1 + i ) − 4 i . We need to identify what the variable i represents in this formula from the given options.
Analyzing the Components Let's analyze the structure of the formula. The term ( 1 + i ) − 4 suggests that i is related to the interest rate applied over a certain period, and the exponent − 4 indicates the number of periods. Since the formula calculates the monthly payment, it's highly likely that i represents the interest rate per month (or per period).
Evaluating the Options Now, let's consider the options: a. annual interest rate: If i were the annual interest rate, we would expect to see it divided by 12 to get the monthly interest rate, which isn't the case here. b. interest rate per period: This aligns with our analysis that i represents the interest rate for the period matching the payment frequency (monthly). c. initial amount: The initial amount is usually represented by P V (present value) in loan formulas. d. incident amount: This doesn't have a standard meaning in the context of loan formulas.
Determining the Answer Based on the formula structure and the options, the most logical answer is that i represents the interest rate per period.
Examples
Understanding loan formulas is crucial in personal finance. For example, if you want to buy a car and need to take out a loan, knowing how the monthly payment is calculated helps you compare different loan offers. By understanding the variables in the formula, such as the interest rate per period, you can make informed decisions about the loan terms and choose the option that best fits your budget. This knowledge empowers you to manage your finances effectively and avoid unexpected costs.
