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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.

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total cost of the watch? you mean car? Also, how is the interest compounded? –  orlandpm Dec 15 '12 at 7:19
    
You say the cost of the car is $\$120,00$ but you probably meant $\$120,000$ –  Henry Dec 15 '12 at 7:28

1 Answer 1

up vote 1 down vote accepted

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 $$120000+\sum_{k=1}^{12} k \times 5000 \times 0.12$$

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