The question says using the formula
P with a small n below it(Pn)
Pn=PMT(1-(1+i)^-n/i) the full parenthesis is divided by the I just to be clear
Pn=present amountborrowed
n=number of monthly pay periods
PMT=monthly payment
i=interest rate per month
A) determine the monthly payment on a 5 year car loan with a monthly percentage rate of .0625% for a car with an original cost of 21000 and 1000 down payment, to the nearest cent.
I set it up as
2000=x(1-(1+(.00625/12)^-5(12)/.00625/12)
when I put this in my calculatori got an error if possible did I make a error?
for part two
x=300(1-(1+(.00625/12)^-5(12)/.00625/12) is how I set it up but I still got a error in my calculator
please help I hope this is enough work to have guidance with!!
thank you so much
you are messing up the percentages.
you have .00625% , l think that has to be just .00625
I think the rate was 7.5% per annum, compounded monthly which will give
us .075/12 = .0625, don't divide it by 12 twice.
I also noticed you had 2000 istead of 20000
your calculation should be
20000=x(1-(1+(.00625)^-60)/.00625)
20000=x(1- 1.00625^-60)/.00625)
Try again.
I got quite a reasonable answer, what did you get ?
I dont know what part two is asking, but I see the same errors
I tried it again and for
A) I did 20,000=PMT(1-(1-.00-.00625/.00625-60)
20,000=PMT(-73.073)
PMT=$273.69
B)PN=300 (1-(1-.00625)/.00625-60)
PN=21921.8227
21922
-2100
$922
Is this now correct? Thank you
Part 2 was asking The affordable monthly payment is $300 for the same time period. Determine an appropriate down payment, to the nearest dollar.
As the work seen above I got $922
No
20000=x(1- 1.00625^-60)/.00625)
20000 = x(49.905308..)
x = $400.76
for the 2nd part, find the present value of 60 payments of $300
PV = 300(1 - 1.00625^-60)/.00625
= 14971.59
since you were buying a $21,000 car you will need a downpayment of
21000-14971.59
or $ 6028.41
To help you solve the problem, let's break it down step by step.
First, let's clarify the given information:
- Original cost of the car: $21,000
- Down payment: $1,000
- Loan period: 5 years (which means 60 monthly payments)
- Monthly interest rate: 0.0625% or 0.000625 (since it's given as a percentage)
Now, let's calculate the monthly payment (PMT) using the formula you provided:
Pn = PMT * (1 - (1 + i)^-n / i)
Substituting the given values:
Pn = PMT * (1 - (1 + 0.000625)^-60 / 0.000625)
Now, let's simplify the equation further:
Pn = PMT * (1 - (1.000625)^-60 / 0.000625)
To solve for PMT, divide both sides of the equation by the expression [(1.000625)^-60 / 0.000625]:
PMT = Pn / (1 - (1.000625)^-60 / 0.000625)
Now, let's plug in the values and calculate the monthly payment amount for the car loan:
PMT = 20,000 / (1 - (1.000625)^-60 / 0.000625)
= 20,000 / (1 - 0.96103514)
Simplifying further:
PMT = 20,000 / 0.03896486
≈ 513.19
So, the monthly payment on the 5-year car loan, to the nearest cent, is approximately $513.19.
For the second part of the question, you have the same formula but with a different value. Let's calculate it:
PMT = 300 / (1 - (1.000625)^-60 / 0.000625)
= 300 / (1 - 0.96103514)
= 300 / 0.03896486
≈ 7,694.21
So, the monthly payment for the second part of the question is approximately $7,694.21.
Make sure to double-check the values you are entering into your calculator, as errors often occur due to mistyped numbers or misplaced decimal points.