Question

You have saved $15,000 for down payment on a car costing $55,000, and plan to finance the rest with a 5-year loan. The dealer is offering you a loan with a monthly payment of $1,050. What effective annual rate of interest is the dealer charging on the loan

Answer 1

1,050 * 60 = 63,000

63,000 - 40,000 = 23,000

I = PRT
23,000 = 40,000 * R * 5
23,000 = 200,000R
23,000 / 200,000 = R
0.115 = R

11.5% = R

Answer 2

so you are financing 55000 - 15000, or
40000
so let the monthly rate be i

1050(1 - (1+i)^-60)/i = 40000

payment = 40000/( 1 - (1+i)^-60)/i

checking for some interest rates
let i = 0, (no interest)
payment = 40000/60 = 666.67
let i = .005 , (6% interest)
payment = 40000/ (1 - 1.005)^-60)/.005) ) = 773.31
let i = .01 (12% interest)
payment = 40000/((1 - 1.01)^-60)/.01) = 889.78
let i = .015 (18% interest)
payment = 40000/(1 + 1.015)^-60)/.015 = 1015.73

so it looks like around 18%
let's fine-tune it a bit more

let i = .016
payment = 40000/(1 - 1.016)^-60)/.016) = 1042
just a bit more....
let i = .017
payment = ... = 1068.67 , a bit too high

let i = .0165
payment = ... = 1055.31

let i = .0164
payment = ... = 1052.64

can you see what I am doing.
with a good calculator you can get the i as close as you want
I am guessing around i = .0163 to get a payment of 1049.99

wow, that's close
so the annual rate is 12(.0163) = .1956 or 19.56 %

Answer 3

Sam had $5000 cash for a down payment on a car. He took out a loan at 9% per annum, compounded monthly to pay for the rest. His monthly payments will be $445.20 for the next 3 years. What is the price of the car?