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July 3rd, 2018, 03:28 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  How are this direct steps written?
A sum of money was invested for 14 years in Scheme A, which offers simple interest 8% p.a. The amount received from Scheme A was then invested for 2 years in Scheme B, which offers compound interest (with annual compounding) at a rate of 10% p.a. If the interest received from Scheme B was Rs 6678, what was the sum invested in Scheme A? Solution: 100 + 112 = 212 6678 * 100/21 * 100/212 = 15000 Last edited by skipjack; July 4th, 2018 at 12:01 AM. 
July 3rd, 2018, 05:12 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
Take the original amount to be "S". Then at 8% simple interest, in 14 years it will have drawn (14)(0.08 )(S)= 1.12S in interest and the total amount, including the original amount, is 1.12S+ S= 2.12S. That is now invested at compound interest of 10%, compounded annually, for 2 years. Since that is only 2 years, it is simpler to calculate the amount after each year rather than use a formula. The interest for the first year is (0.10)(2.12S)= 0.212S. The total amount is, 0.212S+ 2.12S= 2.332S. The interest for the second year is (0.10)(2.332S)= 0.2332S so the total interest, for the two years, is 0.212S+ 0.2332S= 0.4452S. We are told that the interest was 6678. 0.4452S= 6678 so S= 6678/0.4452= 15,000.

July 3rd, 2018, 06:01 AM  #3  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,466 Thanks: 949  Quote:
If you are unable to solve, then nothing will be gained through explaining how the given "shortcut solution" was arrived at. Last edited by skipjack; July 4th, 2018 at 12:07 AM.  

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