SOLUTION: Nicole borrowed $2500 from a bank for 17 months. The bank discounted the loan at 5.1%. What is the loan's discount? What is the net amount of money Nicole receives? What is the loa

Algebra ->  Finance -> SOLUTION: Nicole borrowed $2500 from a bank for 17 months. The bank discounted the loan at 5.1%. What is the loan's discount? What is the net amount of money Nicole receives? What is the loa      Log On


   

Question 1181213: Nicole borrowed $2500 from a bank for 17 months. The bank discounted the loan at 5.1%. What is the loan's discount? What is the net amount of money Nicole receives? What is the loan's actual rate of interest? (To the nearest hundredth of a percent)
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
Here's how to calculate the loan's discount, net amount, and actual interest rate:
**1. Calculate the discount:**
* **Convert the time to years:** 17 months / 12 months/year ≈ 1.4167 years
* **Discount = Principal * Rate * Time**
* Discount = $2500 * 0.051 * 1.4167
* Discount ≈ $180.21
**2. Calculate the net amount of money Nicole receives:**
* **Net Amount = Principal - Discount**
* Net Amount = $2500 - $180.21
* Net Amount ≈ $2319.79
**3. Calculate the loan's actual rate of interest (also called the effective interest rate or APR):**
The actual interest rate is the interest paid (the discount) expressed as a percentage of the net amount received, over the loan period.
* **Actual Interest Rate = (Discount / Net Amount) / Time**
* Actual Interest Rate = ($180.21 / $2319.79) / 1.4167
* Actual Interest Rate ≈ 0.0777 * 0.7058 ≈ 0.0548
* Actual Interest Rate ≈ 0.0548 * 100% ≈ 5.48%
**Answers:**
* Loan's discount: Approximately $180.21
* Net amount Nicole receives: Approximately $2319.79
* Loan's actual rate of interest: Approximately 5.48%