Question
You have arranged for a loan on your new car that will require the first payment today. The loan is for $38,500, and the monthly payments are $690.
If the loan will be paid off over the next 69 months, what is the APR of the loan? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
If the loan will be paid off over the next 69 months, what is the APR of the loan? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Answers
In the standard compound interest formulas, the payment is made at the end of the month.
So I will consider today's payment to be a down payment.
Balance owing = 38500-690 = 37810
let the monthly rate be i
the number of payments = 68
690( 1 - (1+i)^-68)/i = 37810
There is no easy algebraic way to solve that type of equation.
I will use Wolfram to get it, I switched my i to x to avoid confusion with
complex numbers.
Wolfram said: the monthly rate is .00651317
so the annual rate compounded monthly is .07815804 or 7.82%
So I will consider today's payment to be a down payment.
Balance owing = 38500-690 = 37810
let the monthly rate be i
the number of payments = 68
690( 1 - (1+i)^-68)/i = 37810
There is no easy algebraic way to solve that type of equation.
I will use Wolfram to get it, I switched my i to x to avoid confusion with
complex numbers.
Wolfram said: the monthly rate is .00651317
so the annual rate compounded monthly is .07815804 or 7.82%