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July 3rd, 2018, 02:28 AM   #1
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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 3rd, 2018 at 11:01 PM.
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July 3rd, 2018, 04:12 AM   #2
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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.
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July 3rd, 2018, 05:01 AM   #3
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Quote:
Originally Posted by Ganesh Ujwal View Post
A sum of money was invested for 14 years in Scheme A, at 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?
Please show YOUR solution (assume no solution was given).

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 3rd, 2018 at 11:07 PM.
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