Question

A dealer offers a $35,000 car with a downpayment of $3,000 and 65 easy monthly payments of $539.99. How much monthly interest rate is he charging?

Answer 1

0.285%

Explanation:

Given,

The original value of the car = $ 35,000,

Amount of down payment = $ 3000,

So, the principal amount of the loan, P.V. = 35,000 - 3,000 = $ 32,000

Now, the amount of each monthly payment P= $ 539.99,

Number of monthly payments, n = 65,

Since, the monthly payment formula is,

`P=(PV(r))/(1-(1+r)^(-n))`

Where, r is the monthly interest rate,

`539.99 =(32000(r))/(1-(1+r)^(-65))`

By graphing calculator,

`r=0.00285 = 0.285\%`

Thus, he is being charged 0.285 % interest per month.

Answer 2

9.68%

Explanation:

cost of car = $35,000

down payment = $3,000

number of monthly instalments= $65

amount in every monthly instalment= $539.99

total monthly payment= 65×539.99= 35099.35

amount to be paid apart from downpayment= $35,000-3000= 32,000

therefore total interest paid in 65 months= 35099.35-3200= $3099.35

now, monthly interest rate
`r= (3099.35)/(32,000)*100`

⇒ r= 9.68%