SOLUTION: A person borrows $3,600 and agrees to repay the loan in monthly installments over a period of 3 years. The agreement is to pay 1% of the unpaid balance each month for using the mon

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Question 760521: A person borrows $3,600 and agrees to repay the loan in monthly installments over a period of 3 years. The agreement is to pay 1% of the unpaid balance each month for using the money and $100 each month to reduce the loan. What is the total cost of the loan over the 3 years?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's calculate how much total interest is paid

1% of 3600 + 1% of 3500 + ... + 1% of 200 + 1% of 100

0.01*3600 + 0.01*3500 + ... + 0.01*200 + 0.01*100

0.01*(3600 + 3500 + ... 200 + 100)

0.01*(100*(36 + 35 + ... 2 + 1))

0.01*100*(1 + 2 + ... + 35 + 36))

1*(1 + 2 + ... + 35 + 36))

1 + 2 + ... + 35 + 36

36*(1+36)/2 ... Note: using formula found here

666

So $666 in interest will be paid on top of the $3600 principal.

3600+666 = 4266

Total Cost of Loan: $4,266