Car loan: 5-yr annual-payment loan with interest rate of 6% per year.
Annual payment = $5,000.
You have just made a payment and decided to pay the loan off by repaying the outstanding balance.
a) what is payoff amount if you have owned the car for one year (so there are 4 years left on the loan)?
b) What is payoff amount if you have owned the car for 4 years (so there is one year left on the loan)?
please help. thank you.
annual payments on a car loan?
Never heard of that, but, anyway.....
Cash value of car = 5000( 1 - 1.06)^-5)/.06
= 21061.82
a)
value of loan after 1 year had you made no payments at all
= 21061.82(1.06) = 22325.53
but you just made a payment of 5000
So balance after one year = 22325.53 - 5000
= 17325.53
b)
value of loan after 4 years had you made no payments at all
= 21061.82(1.06)^4
= 26590.06
amount of 4 payments
= 5000( 1.06^4 - 1)/.06
= 21873.08
balance after 4 years
=26590.06 - 21873.08
= 4716.98
check: interest on that last balance
= 4716.98(.06) = 283.02
last payment = 4716.98+ 283.02 = 4999.998
not bad eh??
To calculate the payoff amount, we need to consider two components: the remaining principal balance and any interest accrued.
a) To calculate the payoff amount if you have owned the car for one year (so there are 4 years left on the loan), we first need to calculate the remaining principal balance.
Step 1: Calculate the initial loan amount.
Since this is a 5-year loan with an annual payment of $5,000, the initial loan amount would be:
Initial loan amount = (Annual payment) x (Number of years)
Initial loan amount = $5,000 x 5
Initial loan amount = $25,000
Step 2: Calculate the annual interest payment.
The annual interest payment can be calculated using the interest rate and the remaining principal balance. In the first year, the remaining principal balance is the initial loan amount.
Annual interest payment = (Interest rate) x (Remaining principal balance)
Annual interest payment = 0.06 x $25,000
Annual interest payment = $1,500
Step 3: Calculate the remaining principal balance after one year.
The remaining principal balance after one year would be the initial loan amount minus the annual payment minus the annual interest payment.
Remaining principal balance after one year = Initial loan amount - Annual payment + Annual interest payment
Remaining principal balance after one year = $25,000 - $5,000 + $1,500
Remaining principal balance after one year = $21,500
Step 4: Calculate the payoff amount.
The payoff amount would be the remaining principal balance plus any interest accrued after one year.
Payoff amount = Remaining principal balance after one year + Annual interest payment
Payoff amount = $21,500 + $1,500
Payoff amount = $23,000
Therefore, if you have owned the car for one year, the payoff amount would be $23,000.
b) To calculate the payoff amount if you have owned the car for 4 years (so there is one year left on the loan), we follow a similar process.
Step 1: Calculate the remaining principal balance after 4 years.
To calculate the remaining principal balance after 4 years, we need to subtract the annual payments made for 4 years from the initial loan amount.
Remaining principal balance after 4 years = Initial loan amount - (Annual payment x Number of years)
Remaining principal balance after 4 years = $25,000 - ($5,000 x 4)
Remaining principal balance after 4 years = $5,000
Step 2: Calculate the annual interest payment for the final year.
The annual interest payment for the final year would be the remaining principal balance after 4 years multiplied by the interest rate.
Annual interest payment for the final year = Remaining principal balance after 4 years x Interest rate
Annual interest payment for the final year = $5,000 x 0.06
Annual interest payment for the final year = $300
Step 3: Calculate the payoff amount.
The payoff amount would be the remaining principal balance after 4 years plus any interest accrued in the final year.
Payoff amount = Remaining principal balance after 4 years + Annual interest payment for the final year
Payoff amount = $5,000 + $300
Payoff amount = $5,300
Therefore, if you have owned the car for 4 years, the payoff amount would be $5,300.