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"Suppose that you borrow $1000 that you promise to pay back in 12 monthly installments of $100 each. What rate of interest are you paying? At first glance it seems that your interest rate is 20 %: you have borrowed $1000, and you are paying back $1200. But this analysis is
incorrect. For you haven't really borrowed $1000 for an entire year. You have
borrowed $1000 for a month, and then you pay back $100. Then you only
have borrowed $900, and you owe only a month's interest on the $900. You
borrow that for a month and then pay back another $100. And so on.
The stream of payments that we want to value is
(1000, -100, -100, . . . , -100). We can find the interest rate that makes the present value of this stream equal to zero by using a calculator . The actual interest rate that you are paying on the installment loan is about 35 percent! "

QUESTION : I do not understand how he found it! What i am doing is the following :
1000 + (-100) / (1+r) + (-100)/(1+r)^2+ (-100)/(1+r)^3 + (-100)/(1+r)^4 + ... + (-100)/(1+r)^12 = 0.
But this doesn't give r = 35 % ! (r = interest rate). How did he found it ?
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  #2 (permalink)
: The 100 for 12 months figure a a simple interest loan, for a composite interest yo calculate the dally balance and the % interest rate divided by the number of days (365 for a year), any payment apply first to the interest earned and whatever is left after that apply to the principal
Thats the method used by credit cards, the goal for the lender is to make the payment small so very little money goes to pay off the principal, in that way the debt can produce interest payments for a long time.

Some other calculate the whole interest amount, for instance 1000 at 20% for a year would be 200, then set the balance at 1200 and apply your 2 first payments to interest only, I'm not sure if this is legal even if you agreed to it on the credit contract.

Some other financial companies like for instance CITI apply the day by day method but report principal plus interest to the credit bureaus, a loan for 10,000 with them will appear as a maybe 15,000 on your report worsening your debt to credit ratio and lowering your scores even further
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