Question

John bought a car worth $29,000 by taking a bank loan. He pays $5,000 initial deposit and agrees to pay $600 at the beginning of each month as long as necessary. What is the number of full payments he needs to make if interest is J12 = 12%? Select one: A. 50 B. 52 C. 49 D. 51

Answer 1

The number of full payments he needs to make is 51.

Step-by-step explanation:

We are given that John bought a car worth $29,000 by taking a bank loan. He pays $5,000 initial deposit and agrees to pay $600 at the beginning of each month as long as necessary.

So, according to the question;

Amount of the car = $29,000

Initial deposit made by John = $5000

Amount left to be paid = $29,000 - $5,000

                                     = $24,000

Now, Payment which has to be paid per month = $600

The Interest rate is given = 12%

The Monthly interest rate will be = r =  $\frac{0.12}{12}$  = 0.01

Now, the Future value of the amount is given by;

     Future value = $\text{Payment per month} \times \frac{(1+r)(1-(1+r)^{-n}) }{r}$

        $24,000  =  $600 \times \frac{(1+0.01)(1-(1+0.01)^{-n}) }{0.01}$  

         $\frac{24,000}{60,000}= (1.01)\times (1-(1.01)^{-n})$

         $0.4= (1.01)\times (1-(1.01)^{-n})$

          $(1.01)^{-n}= 1 - \frac{0.4}{1.01}$

           $(1.01)^{-n}= 0.604$

Now, taking log both sides we get;

          $-n \times ln(1.01) = ln(0.604)$  

                $n = -\frac{ln(0.604)}{ln(1.01)}$

                n = 50.66 ≈ 51 payments

Hence, the number of full payments John needs to make is 51.