To solve this problem using a financial calculator, you'll need to determine a few key variables:
- N: The total number of payments (monthly payments over the entire loan term).
- PV: The present value (the amount borrowed).
- FV: The future value (the remaining balance after a certain number of payments).
- i/y: The interest rate per period (monthly interest rate).
- PMT: The monthly payment amount.
Step 1: Calculate Monthly Payment (PMT)
-
N: Total number of months for the loan. \[ N = 6 \text{ years} \times 12 \text{ months/year} = 72 \text{ months} \]
-
PV: Principal amount of the loan. \[ PV = -43,312.00 \text{ (negative because it's an outgoing payment)} \]
-
i/y: Monthly interest rate. \[ \text{Annual interest rate} = 6.11% \] \[ i/y = \frac{6.11%}{12} = 0.50917% \] (as a decimal, \(0.50917% = \frac{0.0611}{12} \approx 0.0050917\))
-
Use the calculator to compute PMT for 72 periods:
- Set the calculator to \(N = 72\), \(PV = -43,312\), \(i/y = 0.50917%\), and \(FV = 0\).
- Calculate PMT.
Step 2: Calculate the Remaining Balance after 16 Payments
After finding the PMT, we will compute the remaining balance after 16 payments:
-
N: Number of payments made, which is 16.
-
PV: Calculate the future value after 16 payments to find the remaining balance. Set \(PMT\) to the value computed in Step 1.
-
After making 16 payments, use: \[ N = 72 - 16 = 56 \text{ remaining payments} \]
-
FV: You want to find the future value (the remaining loan balance after 16 payments).
Complete the Calculator Setup
-
For PMT Calculation
- N: 72
- PV: -43,312
- i/y: 0.50917
- FV: 0
-
For Remaining Balance Calculation
- N: 16
- PV: -43,312 (or the previously computed balance if using the original setup)
- PMT: (value found)
- i/y: 0.50917
- FV: Calculate to find the remaining balance.
Using these steps, you will be able to find out how much Derek would still owe after 16 months if he wants to pay off his car loan.
1 answer