SOLUTION: In 7 years I want to buy a car which most likely will cost 40,000.00. The bank offers an APR of 4.5%. How much monthly deposits I will need to make to come up with 40,000.00?

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Question 1132676: In 7 years I want to buy a car which most likely will cost 40,000.00. The bank offers an APR of 4.5%. How much monthly deposits I will need to make to come up with 40,000.00?
Found 3 solutions by jerryguo41, MathTherapy, greenestamps:
Answer by jerryguo41(197) About Me  (Show Source):
You can put this solution on YOUR website!
The monthly payment can be found by using the following formula:
M+=+%28P%281%2Br%29%5En%2Ar%29%2F%28%281%2Br%29%5En-1%29
where
P = Present Value (beginning value or amount of loan)
r = Periodic Interest Rate = APR/ # of interest periods per year
M = Monthly Payment
n = # of interest periods for overall time period (i.e., interest
periods per year * number of years)

Plugging in your values, you would get.
r+=+0.045%2F12
r+=+0.00375
PLuging in "r"
M+=+%28P%281%2Br%29%5En%2Ar%29%2F%28%281%2Br%29%5En-1%29
M+=+%2840000%281%2B0.00375%29%5E84%2A%280.00375%29%29%2F%28%281%2B0.00375%29%5E84-1%29
M+=+%28205.4178%29%2F%28%281%2B0.00375%29%5E84-1%29
M+=+%28205.4178%29%2F%28.3695%29
M+=+556.009
In Money:
$556.01 per month for 84 months. You end up paying a total of $46,704.54 and pay $6,704.54 in interest.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
In 7 years I want to buy a car which most likely will cost 40,000.00. The bank offers an APR of 4.5%. How much monthly deposits I will need to make to come up with 40,000.00?
Correct answer: You need monthly deposits of highlight_green%28%22%24406.01%22%29 in order to accumulate $40,000 in 7 years.

ACCEPT no other ANSWER!!

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Tutor @jerrygou41 answered the wrong problem -- finding the monthly payment you would have if you took a loan for 7 years at 4.5% compounded monthly.

Tutor @MathTherapy gave you the correct answer without showing how to get it; if you actually wanted to learn how to solve a problem like this, that response would of course be of no use to you.

Here is one form of the formula you can use to find the monthly deposit required "A" to accumulate a value of $40,000 in 7 years at 4.5% interest compounded monthly:

40000=+A%28%281%2B.045%2F12%29%5E%28%2812%2A7%29%29-1%29%2F%28.045%2F12%29

It is easy to get parentheses in the wrong places when solving the problem using that formula; I suggest doing the calculations for finding A as follows:

(1) 1+.045/12
(2) to the power 84
(3) -1
(4) divided by (.045/12) [parentheses critical there!]
(5) 40000 divided by that number