SOLUTION: You can afford a $300 per month car payment. You've found a 5 year loan at 8% interest.
What the maximum loan could be?
Algebra ->
Finance
-> SOLUTION: You can afford a $300 per month car payment. You've found a 5 year loan at 8% interest.
What the maximum loan could be?
Log On
You can put this solution on YOUR website! .
You can afford a $300 per month car payment. You've found a 5 year loan at 8% interest.
What the maximum loan could be?
~~~~~~~~~~~~~~~~~~~
Use the formula for the monthly payment for a loan
M =
where P is the loan amount; r = is the interest rate per month;
n is the number of payments (same as the number of months); M is the monthly payment.
From this formula, the expression for the maximum loan is
P = .
In this problem M = $300; r = , n = 5*12 = 60 monthly payments.
Substitute these values into the formula and get for the maximim loan amount
P = = $14,795.53.
ANSWER. The maximum loan amount is $14,795.53.
Monthly payment formula
P = (L*i)/( 1-(1+i)^(-n) )
where,
P = monthly payment
L = loan amount
i = monthly interest rate in decimal form
n = number of months
We will plug in:
P = 300
i = 0.08/12 = 0.006666667 approximately
n = 60 (since 5 years = 5*12 = 60 months)
So,
P = (L*i)/( 1-(1+i)^(-n) )
300 = (L*0.006666667)/( 1-(1+0.006666667)^(-60) )
300 = L*0.020276394
L = 300/0.020276394
L = 14795.53021114
L = $14,795.53
Each decimal value is approximate.
You can use an online calculator such as this to confirm. https://www.omnicalculator.com/finance/auto-loan
Type 8 into the interest rate box, 5 into the year box, and 300 into the monthly payment box.
After entering those inputs, the "loan amount" box will go from empty to $14,795.53
(