Question 1152312: You want to purchase a new car. You are offered a loan for $16000 with an annual interest rate of 6% and a 36 month repayment period. Estimate how much your monthly payment would be for this loan. ( Note - It is assumed you will use the average balance method).
Average Balance Method
1)Find the interest on the principal.
I=Principle*Rate*Term
I=16000*.06*3
I=$2880
2)Add that interest to HALF the principle
$2880+$8000=10880
3)Divide that sum by the number of payments
$10880/36=$302.22222 or $302.23 every month. However, this is NOT the correct answer. Please help!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! car loans are usually done by the declining balance monthly compound interest rate formula.
using a financial calculator, i gave it the following inputs.
present value = 16000
future value = 0
monthly interest rate = 6% / 1200 = .005
number of months = 36
payments are made at the end of each month.
i then clicked on future value and the calculator tells me that the monthly payments needs to be $486.7509992.
the total interest will be 36 * that minus 16000 = 1523.035972.
round those numbers to the nearest penny and you get a monthly payment of $486.75 with total interest of $1523.04.
i also used an average daily balance method calculator on the web and, surprisingly, or maybe not so surprisingly, it gave me the same answer.
i also went to the web to find out the average daily balance method that they use.
not so surprisingly, it was different than the method you showed.
the formula you showed will not pay off the loan in 36 months.
36 * 302 = 10,872.
that's less than the amount owed and does not take into account interest on the loan.
here's some references from the web.
https://investinganswers.com/dictionary/a/average-daily-balance-method
https://www.investopedia.com/terms/a/averagedailybalance.asp
https://www.thebalance.com/average-daily-balance-finance-charge-calculation-960236
https://www.calculator.net/credit-card-calculator.html
note that the average daily balance method is equivalent to the declining balance method when there are no additional payments or withdrawals made during each billing cycle.
the average daily balance method takes these fluctuations into account, but if there are no daily fluctuations, then the average daily balance method becomes the same as the declining balance method with monthly compounding, as best i can determine.
also, different banks use different interpretations of the monthly billing cycle.
some actually count the days in the months, while others assume a 30 day month.
also, if the interest rate is compounded daily, then you will get a different answer than if the interest rate is compounded monthly.
in the answer i provide you, monthly compounding is assumed.
bottom line:
try monthly payment of 486.75 with total interest of 1523.04.
here's some results using average daily balance calculators i found on the web.
the first 4 results are based on using the average daily balance calculators i found on the web.
the last result is based on a declining balance method calculator with monthly compounding that i normally use for car loan type payments.
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