An individual is considering the purchase of a used automobi

An individual is considering the purchase of a used automobile. The total price is $6200 with $1240 as a down payment and the balance paid in 48 equal monthly payments with interest at 1 % per month. The payments are due at the end of each month. Compute the monthly payment. $130.45 $180.18 $215.20

Solution

Total price = 6200

Down Payment = 1240

Remaining to pay in installments = 6200 - 1240 = 4960

Le x be the monthly installment

At the end of 1st month the balance will be 4960(1.01) - x

At the end of second month the balance will be ((4960(1.01) - x)(1.01)) - x = 4960(1.01)² - x(1.01) - x

Going by this Balance at the end of 48th month is going to be

4960(1.01)⁴⁸ - x(1.01⁴⁷ + 1.01⁴⁶ + ................+1.01² + 1.01 + 1)

= 7996 - x(1(1.01⁴⁸ - 1)/1.01 - 1) (Using sum of geometric series S_n = u1(rⁿ - 1)/(r-1))

= 7996 - x(1.61 -1)/.01

= 7996 - x(61)

This should be equal to Zero as all the payments are over

7996 - 61x = 0

x = 7996/61 = 131.08 which is close to 130.45

So answer is (1) i.e. 130.45