Find the monthly payment needed to amortize a typical $205,000 mortgage loan amortized over 30 years at an annual interest rate of 5.9% compounded monthly. (Round your answers to the nearest cent.)
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plug in the number for the ti-84 finance section of a calc

To calculate the monthly payment needed to amortize the $205,000 mortgage loan over 30 years at an annual interest rate of 5.9%, compounded monthly, you can use the **Finance** section of the TI-84 calculator, specifically the **TVM Solver** (Time Value of Money Solver).

Here are the steps to plug in the numbers correctly into the TI-84:

### Variables in the TVM Solver:
- **N**: Total number of payments (number of months)
- **I%**: Annual interest rate
- **PV**: Present value (the loan amount)
- **PMT**: Payment per period (what we are solving for)
- **FV**: Future value (should be 0 for a fully amortized loan)
- **P/Y**: Payments per year
- **C/Y**: Compounding periods per year

### Step-by-step procedure:

1. Press **2nd** and then **FINANCE** to access the TVM Solver.
2. Plug in the following values:
   - **N** = $ 30 \times 12 = 360 $ (since there are 30 years, and 12 months per year)
   - **I%** = 5.9 (this is the annual interest rate)
   - **PV** = 205,000 (the loan amount)
   - **PMT** = (this is what we're solving for)
   - **FV** = 0 (the future value is 0 since the loan is fully paid off)
   - **P/Y** = 12 (monthly payments, so 12 payments per year)
   - **C/Y** = 12 (compounded monthly)

3. After entering the values, move the cursor to **PMT** and press **ALPHA** and **ENTER** to solve for the monthly payment.

This will give you the monthly payment.

Let me calculate that for you.The monthly payment needed to amortize the $205,000 mortgage over 30 years at an annual interest rate of 5.9% compounded monthly is approximately **$1,215.93**.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How would the monthly payment change if the interest rate was reduced to 5%?
2. What is the total amount paid over the life of the loan?
3. How much interest is paid in total over the 30 years?
4. How does a shorter loan term, like 15 years, affect the monthly payment?
5. What happens to the monthly payment if the loan amount increases to $250,000?

**Tip:** When calculating a mortgage, small changes in interest rates can have a significant effect on the total interest paid over the life of the loan.

Find the monthly payment needed to amortize a typical $205,000 mortgage loan amortized over 30 years at an annual interest rate of 5.9% compounded monthly. (Round your answers to the nearest cent.)

Calculate the monthly payment to amortize a $205,000 mortgage over 30 years at an annual interest rate of 5.9%, compounded monthly. This detailed solution covers key concepts in loan amortization, including the time value of money and the amortization formula. Suitable for high school students and those studying financial mathematics.

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