Question

Compare the monthly payment amount of Annabelle's dream car at two different car dealerships.

Dealership A: The car costs $30,000, and the loan has an annual interest rate of 4.8%.
Dealership B: The car costs $29,800, and the loan has an annual interest rate of 5.4%.
Determine the monthly payment for each dealership, and decide which is cheaper. Both interest rates are compounded
monthly. Both loans are for 5 years, or 60 months. Assume that there is no down payment.
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Answer 1

Dealership A is cheaper. Hope it helps.

Answer 2

By comparing both the payments we can say that Dealer A is cheaper by $4.50.

Explanation:

Dealership A: The car costs $30,000, and the loan has an annual interest rate of 4.8% for 5 years.

The EMI formula is :

`(p* r*(1+r)^(n) )/((1+r)^(n)-1 )`

Now, p = 30000

r =
`4.8/12/100=0.004`

n =
`5*12=60`

Putting values in formula we get;

`(30000*0.004*(1+0.004)^(60) )/((1+0.004)^(60)-1 )`

=>
`(30000*0.004*(1.004)^(60) )/((1.004)^(60)-1 )`

EMI is = $563.34

Dealership B: The car costs $29,800, and the loan has an annual interest rate of 5.4% for 5 years.

p = 29800

r =
`5.4/12/100=0.0045`

n =
`5*12=60`

Putting values in formula we get;

`(29800*0.0045*(1+0.0045)^(60) )/((1+0.0045)^(60)-1 )`

=>
`(29800*0.0045*(1.0045)^(60) )/((1.0045)^(60)-1 )`

EMI = $567.84

By comparing both the payments we can say that Dealer A is cheaper by $4.50.