Question

Frank purchased a car for $14,870. He made a down payment of $1,640. He applied for a five-year installment loan with an interest rate of 9.6%. What is the total cost of the car after five years?

Answer 1

I am not a fan of such a question. The cost is still $14,870. If the question is meant to ask for "cash outlays" over the five year period, that is a different story. The extra cash is not the "cost of the car", but the "cost of borrowing money".

Answer 2

He purchased the car for $14,870 and paid a down payment of $1,640.
14,870 - 1640 = 13,230
He only financed 13,230
Now you need to find the monthly payment for $13,230 on a five-year loan at 9.6% interest.
Once you know the montlhy payment, multiply it by 60 and add to the down payment. That's the total amount he paid.

Answer 3

In any case, the loan amount is $14,870 minus $1,640. Then, the amount of interest paid on that loan over five years is Loan Amount times (1+0.096)^5.

Answer 4

Well, I am assuming annual compounding here. You can assume monthly compounding, and get Loan Amount times (1 + 0.008)^60.

Answer 5

it depends again if the interest calculated is daily compounded or quarterly compounded or ....

Answer 6

i dont know if the question is lil vague or we are making it complicated ?? let me knowhat grade mathematics it is given under ??

Answer 7

A typical loan has monthly payments, not yearly payments.

Answer 8

I'm so confused lol

Answer 9

yeah makes sense emi's .. i second mathstud 55

Answer 10

Monthly payments or annual payments are not the issue. How is the interest compounded and calculated? Since it does not specify, we can assume monthly compounded or annual compounded. I am showing math for both scenarios.

Answer 11

@kelseylynne54 Start simple. Car costs $14,870. He paid $1,640. Amount still owed = $14,870 - $1,640 = $13,230. This amount was borrowed.

So far ok?

Answer 12

Yes

Answer 13

Now, when you borrow money, you need to pay extra in "interest". Same for car loan or home mortgage or whatever. Someone is lending you money and earning the extra "interest" for lending. In this case, the interest rate is given as 9.6% per year.

Answer 14

So far ok?

Answer 15

Yes

Answer 16

considering it monthly compounded and paid as EMI's
p (1+(r/1200)) power 60
13230 (1 + 0.008) power 60

Answer 17

Now, at that yearly interest, if you borrowed $13,230 for a year, you would need to pay back $13,230 + 9.6% of that amount. That means, you pay $13,230 + $13,230 times 9.6/100 = $14,500.08.

Answer 18

In other words, you paid $1,270.08 in extra interest payment just for the first year.

Answer 19

(13230 (1.008) power 60 ) + 1640 would be the answer

Answer 20

Five years interest would be $13,230 + 5 times $13,230 times 9.6/100 = $19,580.40

Answer 21

So far ok?

Answer 22

Yes

Answer 23

So, the cost of car will be $19,580.40 + $1,640 paid ahead of time. Big assumption is that you paid "all borrowed money and interest at the end of five years.

Answer 24

Now, life gets more difficult. Because the problem states that you borrowed an installment loan. That means, you are making monthly payments as you go.

Answer 25

If you use the formula* for annualized payment based on present value, interest rate, and number of payments, you get that the monthly payment is $278.50. Since There were 60 payments, the total amount paid was
60($278.50) + $1640 = $16,710 + $1,640 = $18,350

See drawing below for formula