What values do I enter for N, PMT, i/y, FV and PV on a finance calculator to solve for the question.

Question

Derek borrows $284,857.00 to buy a house. He has a 30-year mortgage with a rate of 5.33%. After making 113.00 payments, how much does he owe on the mortgage?

Answer 1

To find out how much Derek owes on the mortgage after making 113 payments, you'll need to input the following values into a finance calculator. You will be calculating the remaining balance of the loan, which involves inputting the following variables:

• N (Number of Payments): This will represent the total remaining payments. Since the mortgage term is 30 years, you have a total of \( 30 \times 12 = 360 \) payments. After making 113 payments, the remaining payments will be \( 360 - 113 = 247 \).

• PMT (Payment Amount): You need to first calculate the monthly payment that Derek is making using the loan amount, interest rate, and total number of payments (before the payments are made). The formula for the monthly payment (PMT) is:

  \[ PMT = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1} \]

  where:

  • \( P \) = Loan amount ($284,857.00)
  • \( r \) = Monthly interest rate (annual rate / 12)
  • \( n \) = Total number of payments (360)

  The monthly interest rate \( r \) would be \( \frac{5.33%}{100} / 12 = 0.00444167 \) (approximately).

  Plugging in the numbers:

  \[ PMT = 284857 \times \frac{0.00444167(1 + 0.00444167)^{360}}{(1 + 0.00444167)^{360} - 1} \]

  Calculate this to find the PMT.

• i/y (Interest Rate): This is the monthly interest rate expressed as a percentage. For an annual rate of 5.33%, it would be approximately 5.33%/12 = 0.444167%.

• FV (Future Value): You typically set this value to 0 when calculating the remaining loan balance since you want to know what remains on the loan.

• PV (Present Value): This is the initial loan amount, which is $284,857.00 (make sure to enter it as a negative number since it represents an outgoing cash flow).

Summary of Values:

1. N: 247 (remaining payments)
2. PMT: (calculate using the loan details)
3. i/y: 0.444167
4. FV: 0
5. PV: -284,857.00

Once you input these values (with the PMT calculated earlier), you should be able to solve for the present value of the remaining loan balance after 113 payments. Remember to switch the calculation mode on your calculator to solve for the remaining balance.