ANSWERS: 2

I am assuming a yearly interest rate. At the end of one year, for a principal P, you get P*i as interest, where i is the interest rate. Now for multiple years, you can either get each year the same interest (simple interest calculation) or at the end of each year, you CAPITALIZE the interest of the past year, as to earn also in the future some interest on that added sum. This is the compound interest calculation.  I found out that your first example uses a simple interest calculation: 6 * P * (1,0575  1) = 1200 P = (1200/6)/(1,0575  1) P ~ 3478,26  Further information: http://www.investopedia.com/articles/investing/020614/learnsimpleandcompoundinterest.asp

8212017 1. Mr. Smith (proper nouns are capitalized) earned $1200 interest on an investment over 6 years at 5.75%. How much money did he INVEST? (The answer my book provides, says "$3,478.26") * Insufficient information. When you discuss interest you have to be very specific about how it is calculated. Simple interest is a constant interest rate, not added to the principle. So we have A x 0.0575 x 6 = $1200 total interest, and A = $1200/(0.0575 x 6) = $3478.26 so we conclude that this problem is dealing with simple interest. But you can only know that if you are given the answer.
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