car payment problem for math class?
so if i take a loan of $19,990 at 10.21% interest rate for 6 yrs, how much money would i end up paying in total after 6 years? doesnt the interest drop down every month? and what formula do i use?
1 second ago - 4 days left to answer
Comments
L = P * sum((1 / (1 + r/12))^t , t = 1 , t = n)
r = annual rate
n = number of payments
L = loan amount
1 / (1 + r/12)) =>
1 / (1 + 0.1021 / 12) =>
1 / (12.1021 / 12) =>
12 / 12.1021
sum(x^t , t = 1 , t = n) = S
S = x + x^2 + .... + x^n
S * x = x^2 + x^3 + .... + x^n + x^(n + 1)
S * x - S = x^(n + 1) - x
S * (x - 1) = x * (x^n - 1)
S = x * (x^n - 1) / (x - 1)
x = 12 / 12.1021
n = 6 * 12 = 72
19990 = P * (12 / 12.1021) * ((12/12.1021)^72 - 1) / ((12/12.1021 - 1)
19990 = P * (12 / 12.1021) * ((12 / 12.1021)^72 - 1) / ((12 - 12.1021) / 12.1021)
19990 = P * (12 / -0.1021) * ((12 / 12.1021)^72 - 1)
19990 = P * (12 / 0.1021) * (1 - (12 / 12.1021)^72)
19990 = P * 117.53183153770812928501469147894 * (1 - 0.54334620377533658940198340131377)
19990 = P * 53.671357048932036505153762823063
19990 / 53.671357048932036505153762823063 = P
P = 372.45192033760519670903199506637
Your monthly payments will be 372.45 dollars.
You'll end up spending 26816.54 dollars over 6 years (when the exact values are taken)