document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=37333>Question 37333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Whats the difference between 'continuous compounding' & 'regular compounding' of interest.Give some examples.\r<BR>\n" );
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document.write( "Expalin me the concepts so that I can apply the formulae.\r<BR>\n" );
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document.write( "I have the Formulae for both.\r<BR>\n" );
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document.write( "Refered to varioius books and net but not clear. one of the pages say'The distinction is like the difference between getting water from a hand pump and getting water from a faucet. With the hand pump, the water flow is broken. With the faucet, it is continuous. The faucet does not necessarily deliver water any faster than the pump. It just delivers it continuously'. Src-http://www.riskglossary.com/link/compounding.htm<BR>\n" );
document.write( "Pls give NUMERICAL examples to clarrify the difference. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #22978 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=22978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Whats the difference between 'continuous compounding' & 'regular compounding' of interest.Give some examples.\r<BR>\n" );
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document.write( "Expalin me the concepts so that I can apply the formulae.<BR>\n" );
document.write( "OK LET ME TY MY HAND AT THIS AND SEE HOW FAR YOU ARE CONVINCED.PLEASE DO GIVE ME A FEED BACK.<BR>\n" );
document.write( "YOU ARE TALKING ABOUT FORMULAE AND YOU KNOW THEM.THERE IS IN FACT ONLY ONE FORMULA  AND ITS LIMITING CASE.LET US TRY TO UNDERSTAND THIS FROM THE FORMULA<BR>\n" );
document.write( "1.SIMPLE INTEREST..FIRST TO GET AT THE DIFFERENCE..<BR>\n" );
document.write( "IF P=SUM=100 SAY....N=NUMBER OF YEARS =3 SAY .....R =RATE OPF INTEREST PER YEAR=10%=0.1 IN FRACTION SAY AND I=SIMPLE INTEREST IS GIVEN BY<BR>\n" );
document.write( "I=PNR=100*3*0.1=30<BR>\n" );
document.write( "AMOUNT TO BE PAID AFTER 3 YEARS =P+I=100+30=130<BR>\n" );
document.write( "2.COMPOUND INTEREST..<BR>\n" );
document.write( "FOR THE SAME DATA AS ABOVE THE FORMULA IS <BR>\n" );
document.write( "A=P{1+(R/T)}^(N*T)....WHERE THE NEW VARIABLE T REPRESENTS THE PERIOD AFTER WHICH THE INTEREST IS COMPOUNDED OR ADDED TO PRINCIPAL WHICH WILL THEN BECOME THE NEW PRINCIPAL VALUE FROM THAT TIME.<BR>\n" );
document.write( "SO LET US CONSIDER FIRST T=1 YEAR ...THAT IS INTEREST IS CALCULATED AT THE END OF EVERY YEAR AND THEN ADDED ON TO PRINCIPAL,WHICH WILL THEN BE THE NEW PRINCIPAL VALUE FOR THE NEXT YEAR.<BR>\n" );
document.write( "BY THIS FOR THE SAME DATA WE GET<BR>\n" );
document.write( "A=100(1+0.1/1)^(3*1)=133.1...AN INCREASE OF 133.1-130=3.1<BR>\n" );
document.write( "WE CAN EASILY SEE FROM THE FORMULA THAT AS N THE NUMBER OF YEARS INCREASES COMPOUND INTEREST INCREASES MORE THAN SIMPLE INTEREST<BR>\n" );
document.write( "THIS IS THE BACK GROUND..NOW FOR OUR STUDY ON CONTINUOUS COMPOUNDING LET US DO THE SAME TYPE OF CALCULATIONS KEEPING N CONSTANT SAY 1 YEAR ONLY BUT INCREASING  T THE PERIOD OF COMPOUNDING.<BR>\n" );
document.write( "LET US TAKE T=1 AS ABOVE FOR THE BASE CASE ..WE GET <BR>\n" );
document.write( "A=100(1+0.1/1)^(1*1)=110 <BR>\n" );
document.write( "CASE 1.........T=2...THAT IS IN THE SAME 1 YEAR DURATION ,WE CALCULATE THE INTERST IN 2 PERIODS THAT IS 2 HALF YEARS FOR COMPOUNDING..THEN WE GET <BR>\n" );
document.write( "A=100(1+0.1/2)^(1*2)=110.25<BR>\n" );
document.write( "CASE 2.........T=4...THAT IS IN THE SAME 1 YEAR DURATION ,WE CALCULATE THE INTERST IN 4 PERIODS THAT IS 4 QUARTER YEARS FOR COMPOUNDING..THEN WE GET <BR>\n" );
document.write( "A=100(1+0.1/4)^(1*4)=110.3813......ETC..<BR>\n" );
document.write( "LIKE THIS WE  CAN CONTINUE AND WE FIND THAT THE AMOUNT AFTER 1 YEAR INCREASES PROGRESSIVELY AS THE PERIODS OF COMPOUNDING ARE INCREASED.<BR>\n" );
document.write( "NOW WE POSE A THEORETICAL LIMITING QUESTION ?WHAT IS THE MAXIMUM WE CAN GET..AS WE FURTHER INCREASE THE PERIODS TO 12 THAT IS EVERY MONTH...TO 365 THAT IS EVERY DAY...EVERY HOUR...EVERY MINUTE...EVERY SECOND.... ETC....ETC...SUPPOSE INFINITE PERIODS AS A THEOIRETICAL MAXIMUM WHICH IS THEN CALLED \"C O N T I N U O U S C O M P O U N D I N G \"...AS YOU CAN SEE IT IS PURELY THEORETICAL LIMITING CASE AND NO BODY DOES THAT IN PRACTICE IN BUSINESS....THE ANSWER WOULD BE <BR>\n" );
document.write( "A=100(1+0.1/T)^(1*T).....LIMIT AS T TENDS TO INFINITY<BR>\n" );
document.write( "WE TOOK P=100 FOR CONVENIENCE ...IF WE DROP THAT OR TAKE P=1 AND ALSO R=100% OR 1 IN FRACTION<BR>\n" );
document.write( "WE GET <BR>\n" );
document.write( "A=LIMIT T TENDING TO INFINITY OF (1+1/T)^T FOR THE SO CALLED CONTINUOUS COMPOUNDING ...ITS VALUE YOU WOULD KNOW IN STUDY OF FUNCTIONS AND THEIR LIMITS AS EQUAL TO E=2.718282 APPROXIMATELY.<BR>\n" );
document.write( "WELL THIS IS WHAT IS MEANT BY CONTINUOUS COMPOUNDING ..IT IS A THEORETICAL LIMTING CONCEPT... </SPAN>\n" );
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