The simple interest for 10 years is Rs. 6,000. The compound interest
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08 Jun 2021, 07:01
The key is to understand the difference between Simple Interest and Compound interest (compounded annually) from year 1 to year 2.
Given the same Original Investment of money (call it P) into two different accounts with the same interest rate (call it R), let the two different accounts be:
Account X (which pays R% simple interest annually)
and
Account Y (which pays R% compound interest, compounded annually)
At the End of Year 1:
Interest Earned in Account X = Interest Earned in Account Y
Since the R% will be applied to just the original investment P in both the simple interest and compound interest accounts ———-> interest earned = (R%) (P)
And there will be no “interest upon interest” earned in the compound interest account Y in year 1
Since the simple interest account X earned $6,000 in total over 10 years, this means that ($6,000/10) = $600 was earned at the end of Year 1 in each account.
Since the Total Interest earned after 2 years in the compound interest account Y was $1,400, this means the annual Compound Interest earned only in Year 2 must have been ——->
(total interest earned in 2 years) - (interest earned at end of year 1) =
$1,400 - $600 = $800
At the End of Year 2:
the simple interest account will again earn R% interest on the original investment P. From above, we know that this amount equals = (R%) (P) = $600
for the compound interest account Y, we already know that $800 interest was earned only in Year 2. This compound interest earned in Year 2 will be composed of 2 parts:
(Part 1) The interest rate R% applied to the original investment P =
(R%) (P)
AND
(Part 2) “interest earned on interest”: the annual interest rate R% will also be applied on the $600 in interest sitting in the account earned at the end of year 1 =
(R%) ($600)
Again, the total interest earned in year 1 in the compound interest account Y = $800
Thus:
(R%) (P) + (R%) ($600) = $800 —(eq I)
we know from above that the simple interest earned in account X at the end of each year is the annual interest rate R% applied to the original investment P, which equals = (R%) (P) = $600
substitute in $600 = (R%) (P) into (eq I)
$600 + (R%) ($600) = $800
(R/100) (600) = 200
6 * R = 200
R = 33.333333333
Interest Rate R% = 33 and 1/3 %
Lastly, to find the amount of the Original Investment, apply the annual interest rate R% = 33.33% to the original investment and set it equal to the simple interest of $600 earned each year in account X
(33.33%) (P) = $600
(1/3) (P) = $600
P = $1,800
Final Answer:
$1,800
33 and 1/3 %
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