May 21st, 2018, 10:16 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  How they combine two C I equations in single step?
Naveen lends 30000 to Ravi for 2 years at 20% p.a on compound interest on condition that the interest is compounded half yearly for the first year and compounded annually for the second year. What will be the total interest earned by Naveen at the end of two years? Solution: 30000 [1+10/100]^2 x [1+20/100]  30000 = 13560 How they combine two C I equations in single step? Last edited by skipjack; May 25th, 2018 at 02:00 PM. 
May 22nd, 2018, 04:41 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 895 
30000[1+ 10/100]^2 is the principle after the first year compounded twice at (20%)/2= 10%= 10/100 interest each time. Then (30000[1+ 10/100]^2)(1+ 20/100) is that amount at 20% interest for the second year. Subtracting the original principle, 30000, gives the interest that has accrued.

May 22nd, 2018, 05:48 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,791 Thanks: 970 
30000(1.10) = 33000 33000(1.10) = 36300 = 30000(1.10)^2 36300(1.20) = 43560 
May 22nd, 2018, 09:03 AM  #4 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
May 22nd, 2018, 09:55 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,791 Thanks: 970 
Well, if you can't see that what I'm showing is 43560 (final amount)  30000 (start amount) = 13560 (answer), then you may as well give up on this kind of problem... 
May 22nd, 2018, 09:58 AM  #6 
Senior Member Joined: Sep 2015 From: USA Posts: 2,264 Thanks: 1198  
May 22nd, 2018, 06:35 PM  #7 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
May 22nd, 2018, 06:42 PM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,791 Thanks: 970 
No.

May 22nd, 2018, 07:47 PM  #9 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
May 23rd, 2018, 12:49 AM  #10 
Senior Member Joined: Apr 2014 From: UK Posts: 895 Thanks: 328  

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