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Jessicab25
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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%

Verified Answer :

Answer: C. 5.9 %      

Step-by-step 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, \(P = \frac{r/2(PV)}{1-(1+r/12)^{-n}}\)

⇒  \(352 = \frac{r/2(18349)}{1-(1+r/12)^{-60}}\)

⇒  \(1-(1+r/12)^{-60} = \frac{r/2(18349)}{352}\)

⇒ \(1-(1+r/12)^{-60} = \frac{52.1278409091 r}{2}\)

⇒ \(1-(1+r/12)^{-60} = 26.0639204545 r\)

⇒ \(1-(1+r/12)^{-60} - 26.0639204545 r =0\)

⇒ r = 0.0568 = 5.68 % ≈ 5.7%

Since, 5.7% is near to 5.9%.

Thus, the correct answer is C.


JeanaShupp

Answer:  c. 5.9%

Step-by-step explanation:

Given: Present value of loan PV = \(21,349 - 3,000 = 18,349\)

The monthly payment M = 352  

Total number of periods=\(n = 12\times 5 = 60\)


Let the APR  be 'i'.

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

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

By using calculator, we get

\(r=0.568\approx0.59\)

In percent, r= 5.9%

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