Question 1172981
To determine the annual interest rate for this loan, we'll need to use a financial calculator or spreadsheet software because this calculation involves finding the interest rate that satisfies the loan payment formula.

Here's how we can approach it:

**1. Understand the Loan Details:**

* Principal (P): $5,000
* Number of Payments (n): 36 months
* Monthly Payment (PMT): $162.50

**2. Use the Loan Payment Formula (or a Financial Calculator/Spreadsheet):**

The loan payment formula is:

PMT = P [ i(1 + i)^n ] / [ (1 + i)^n  -  1]

Where:

* PMT = Monthly payment
* P = Principal loan amount
* i = Monthly interest rate
* n = Number of payments

We need to solve for 'i'. This is difficult to do algebraically, so we'll use a financial calculator or spreadsheet function.

**3. Using a Financial Calculator or Spreadsheet (Excel, Google Sheets):**

* **Financial Calculator:**
    * Input the following:
        * n = 36
        * PV = 5000
        * PMT = -162.50 (Note: PMT is negative because it's a cash outflow)
        * FV = 0
        * CPT I/Y (or I/YR)
    * The result will be the monthly interest rate. Multiply it by 12 to get the annual rate.
* **Excel/Google Sheets:**
    * Use the `RATE` function:
        * `=RATE(nper, pmt, pv, [fv], [type], [guess])`
        * `=RATE(36, -162.50, 5000)`
    * This will give you the monthly interest rate. Multiply it by 12 to get the annual rate.

**4. Calculation**

Using the rate function in excel, the monthly rate is approximately 0.0125, or 1.25%.

1.25% * 12 = 15%

**Result:**

The annual interest rate is approximately 15%.