Question

Teresa is buying a car for $23,550. She will finance $19,600 of it with a 2-year loan at 2.7% APR. What will her monthly auto payment be?

Answer 1

Monthly payment is $839.83

Explanation:

Given : Teresa is buying a car for $23,550. She will finance $19,600 of it with a 2-year loan at 2.7% APR.

To find : What will her monthly auto payment be?

Solution :

Formula of monthly payment,

Monthly payment,
`M=\frac{\text{Amount}}{\text{Discount factor}}`

Discount factor
`D=(1-(1+i)^(-n))/(i)`

Where, Amount = $19,600

Rate r= 2.7%=0.027

`i=(0.027)/(12)=0.00225`

Time = 2 years

`n=2*12=24`

Now, put all the values we get,

`D=(1-(1+i)^(-n))/(i)`

`D=(1-(1+0.00225)^(-24))/(0.00225)`

`D=(1-(1.00225)^(-24))/(0.00225)`

`D=(1-0.94748)/(0.00225)`

`D=(0.0525)/(0.00225)`

`D=23.337`

Monthly payment,
`M=\frac{\text{Amount}}{\text{Discount factor}}`

`M=(19600)/(23.337)`

`M=839.83`

Therefore, Monthly payment is $839.83

Answer 2

Present value of annuity = 12P(1 - (1 + r/12)^-12n) / r
19,600 = 12P(1 - (1 + 0.027/12)^-(2 x 12)) / 0.027
0.027 x 19600 = 12P(1 - (1 + 0.00225)^-24)
529.2 = 12P(1 - (1.00225)^-24)
12P = 529.2 / (1 - 0.9475) = 529.2 / 0.0525
P = 10,077.9995 / 12 = $839.83

Therefore, her monthly payment = $839.83