Answer :
Certainly! Let's walk through the solution step-by-step:
1. Understanding the Problem:
- Paulo took out a discounted loan of [tex]$900. - The loan has an annual simple interest rate of 12%. - We need to find the effective annual interest rate for this discounted loan. 2. Effective Interest Rate (EIR): - The effective annual interest rate is the actual interest earned or paid on the loan or investment after accounting for compounding within the period. - Given that it’s a simple interest loan, we can simplify our calculation without worrying about additional compounding within the year. 3. Effective Annual Interest Rate Calculation: - The formula for effective annual interest rate (EIR) in this context, where simple interest is used, can be straightforwardly taken as the nominal interest rate because we assume no internal compounding periods within the year. - Mathematical formula for effective annual interest rate (EIR) in this case: \[\text{EIR} = \text{Nominal Annual Interest Rate}\] - Given the nominal annual interest rate is 12%, the effective annual interest rate would also be 12%. 4. Result: - Hence, the effective annual interest rate for Paulo’s $[/tex]900 discounted loan at a 12% simple annual interest rate is:
[tex]\[ \text{EIR} = 12\% \][/tex]
So, the effective annual interest rate for the loan is 12%.
1. Understanding the Problem:
- Paulo took out a discounted loan of [tex]$900. - The loan has an annual simple interest rate of 12%. - We need to find the effective annual interest rate for this discounted loan. 2. Effective Interest Rate (EIR): - The effective annual interest rate is the actual interest earned or paid on the loan or investment after accounting for compounding within the period. - Given that it’s a simple interest loan, we can simplify our calculation without worrying about additional compounding within the year. 3. Effective Annual Interest Rate Calculation: - The formula for effective annual interest rate (EIR) in this context, where simple interest is used, can be straightforwardly taken as the nominal interest rate because we assume no internal compounding periods within the year. - Mathematical formula for effective annual interest rate (EIR) in this case: \[\text{EIR} = \text{Nominal Annual Interest Rate}\] - Given the nominal annual interest rate is 12%, the effective annual interest rate would also be 12%. 4. Result: - Hence, the effective annual interest rate for Paulo’s $[/tex]900 discounted loan at a 12% simple annual interest rate is:
[tex]\[ \text{EIR} = 12\% \][/tex]
So, the effective annual interest rate for the loan is 12%.
