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

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

Answer 2

Answer:

Monthly payment is $839.83

Step-by-step 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 $D=\frac{1-(1+i)^{-n}}{i}$  

Where, Amount = $19,600

Rate r= 2.7%=0.027

$i=\frac{0.027}{12}=0.00225$  

Time = 2 years  

$n=2\times12=24$  

Now, put all the values we get,  

$D=\frac{1-(1+i)^{-n}}{i}$  

$D=\frac{1-(1+0.00225)^{-24}}{0.00225}$  

$D=\frac{1-(1.00225)^{-24}}{0.00225}$  

$D=\frac{1-0.94748}{0.00225}$  

$D=\frac{0.0525}{0.00225}$  

$D=23.337$  

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

$M=\frac{19600}{23.337}$  

$M=839.83$  

Therefore, Monthly payment is $839.83