Question

David is buying a new car for 21,349.00. he plans to make a down payment of 3,000.00. if hes to make monthly payments of 352 for the next five years, what APR has he paid?

a. 5%
b. 59%
c. 5.9%
d. .05%

Answer 1

Answer: c. 5.9%

Explanation:

Given: Present value of loan PV =
`21,349 - 3,000 = 18,349`

The monthly payment M = 352

Total number of periods=
`n = 12* 5 = 60`

Let the APR be 'i'.

Now, the formula to find the monthly payment is given by ;-

`M=((r)/(2)PV)/(1-(1+(r)/(12))^(-n))\\\\\Rightarrow1-(1+(r)/(12))^(-n)=((r)/(2)PV)/(M)\\\\\Rightarrow1-(1+(r)/(2))^(-60)=((r/12)18349)/(342)\\\\\Rightarrow1-(1+(r)/(12))^(-60)-0.2639204545r=0`

By using calculator, we get

`r=0.568\approx0.59`

In percent, r= 5.9%

Answer 2

Answer: C. 5.9 %

Explanation:

Here, the Present amount of loan, PV = 21,349 - 3000 = 18,349

Monthly payment, P = 352

Total number of periods, n = 12\times 5 = 60

Let the APR = r

Since,
`P = (r/2(PV))/(1-(1+r/12)^(-n))`

⇒
`352 = (r/2(18349))/(1-(1+r/12)^(-60))`

⇒
`1-(1+r/12)^(-60) = (r/2(18349))/(352)`

⇒
`1-(1+r/12)^(-60) = (52.1278409091 r)/(2)`

⇒
`1-(1+r/12)^(-60) = 26.0639204545 r`

⇒
`1-(1+r/12)^(-60) - 26.0639204545 r =0`

⇒ r = 0.0568 = 5.68 % ≈ 5.7%

Since, 5.7% is near to 5.9%.

Thus, the correct answer is C.