Commercial Mathematics. A question on payment.

Question

Please help me out with this problem.

Charlie buys a car for \$120,000. He pays half of the amount in cash and agrees to pay the balance in 12 annual instalments of \$5000 each. If the rate of interest is 12% and he pays with the instalment the interest due on the unpaid ammount, find the total cost of the car.

Answer 1

You just need a table of the thirteen payments, which might start something like

Year  Outstanding Interest Instalment Remaining 
  0     120,000        -     60,000    60,000
  1      60,000     7,200     5,000    55,000
  2      55,000     6,600     5,000    50,000

where

• the amount outstanding is equal to the amount remaining the previous year,
• the interest is 12% of the outstanding,
• the instalment is what you specified, and
• the remaining is the the amount outstanding less the instalment.

Then just add up the interest and the instalments.

You would get the same answer with $$120000+\sum_{k=1}^{12} k \times 5000 \times 0.12$$