Question

You are saving money to buy a Car. You will need $20,000 as the price of the car today. If you can make a down payment now of $8000 , and want to pay the rest by installments, A. how much each deposit per month should be if you want to pay the rest of the amount in 24 months if the interest rate on the deposit is 6% per year? B. If you can deposit $664 per month how long will it take you to pay the residual amount from the price of the car? I need the detailed answer please

Answer 1

A.

EMI of loan can be computed as:

EMI = P x r x (1+r) n/(1+r) n – 1

P = Principal of loan = $ 20,000 - $ 8,000 = $ 12,000

r = Rate per period = 0.06/12 = 0.005 p.m.

n = Number of periods = 24 periods

EMI = $ 12,000 x 0.005 x (1+ 0.005)24/ [(1+ 0.005)24-1]

       = $ 60 x (1.005)24/ [(1.005)24-1]

       = $ 60 x 1.12715977620539/ (1.12715977620539-1)

      = $ 60 x (1.12715977620539/ 0.12715977620539)

     = $ 60 x 8.86412205055163

      = $ 531.847323033098 or $ 532

Monthly deposit should be $ 532.

B.

Again, using formula for EMI,

(1+r) n/(1+r) n – 1 = EMI/P x r

(1.005) n/ (1.005) n- 1 = $ 664/ ($ 12,000 x 0.005)

(1.005) n/ (1.005) n- 1 = $ 664/$ 60

(1.005) n/ (1.005) n- 1 = $ 11.06666667

(1.005) n = 11.06666667 x (1.005) n- 1

               = 11.06666667 x (1.005) n - 11.06666667

11.06666667 x (1.005) n - (1.005) n = 11.06666667

(1.005) n x (11.06666667 – 1) = 11.06666667

(1.005) n x 10.06666667 = 11.06666667

(1.005) n = 11.06666667/10.06666667

(1.005) n = 1.099337748

Taking logarithm of both sides and solving for n, we get

n x log 1.005 = log 1.099337748

n x 0.00216606175 = 0.04113114061

n = 0.04113114061/0.00216606175

    = 18.988904914645 or 19 periods

It will take 19 months to pay off the loan on paying $ 664 per month.