Question 1157595: You want to buy a $17,000 car. You can make a 10% down payment and will finance the balance with a 2% interest rate for 48 months (4 years). What will your monthly payments be?
what are the monthly payments
Found 3 solutions by josmiceli, MathTherapy, math_tutor2020:
Answer by josmiceli(19441)   (Show Source):
Answer by MathTherapy(10551)  (Show Source):
You can put this solution on YOUR website!
You want to buy a $17,000 car. You can make a 10% down payment and will finance the balance with a 2% interest rate for 48 months (4 years). What will your monthly payments be?
what are the monthly payments
FINANCING doesn't imply SIMPLE INTEREST!
I'm tired of pointing this out to the other person who responded and he NEVER, EVER changes his approach to these
problems! Maybe as an older person he just doesn't feel that he needs to listen to others and learn from them!
His answer, if you don't know by now, is INCORRECT!
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
@josmiceli is correct in stating the loan is $15,300 (after paying 10%)
However, simple interest is not used (as @MathTherapy has pointed out). So unfortunately the answer of $344.25 is not correct.
Why isn't simple interest used? Because the interest is compounded each month. As part of the monthly payment, you pay off the principal plus interest. The principal is the amount loaned (well the monthly payment is a piece of the overall principal I should say).
You can think of it like this:
You have $15,300 in an account that accrues 2% interest compounded monthly. Over time, you withdraw some fixed amount (we don't know this amount yet). The idea is that we withdraw this amount 48 times over the 48 months, and by the time we reach the end of month 48, we'll hit $0 in the bank account.
As this example shows, the remaining stuff in the account will accrue interest. It's only when we withdraw everything that we won't accrue the compound interest. But if you withdraw everything, then that's effectively paying off the full loan and defeats the whole purpose of spreading payments out.
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The formula to use is this
P = (L*i)/( 1-(1+i)^(-n) )
where,
P = monthly payment
L = 15,300 = loan amount
i = interest rate per month = 0.02/12
n = number of months = 48
So,
P = (L*i)/( 1-(1+i)^(-n) )
P = (15,300*0.02/12)/( 1-(1+0.02/12)^(-48) )
P = 331.9353916819
P = 331.94
Here are 2 calculators that will help confirm the answer (they're basically the same with some slight differences)
https://www.calculator.net/loan-calculator.html
https://www.bankrate.com/calculators/mortgages/loan-calculator.aspx
Both of which are free.
There are tons more options of course, so feel free to use your favorite.
If you want to calculate this using Excel (or similar programs such as OpenOffice spreadsheet), then you would type in this formula
=PMT(0.02/12,48,15300,0,0)
Don't forget about the leading equal sign.
Consult the help manual for this PMT function if you're curious what each of the entries do.
Answer: $331.94
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