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The simple interest for 10 years is Rs. 6,000. The compound interest
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08 Jun 2021, 06:15
08 Jun 2021, 06:15
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Difficulty:
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Question Stats:
69% (02:02) correct
31%
(02:55)
wrong
based on 59
sessions
The simple interest for 10 years is Rs. 6,000. The compound interest for 2 years is Rs. 1,400. Find the rate of interest and the principal.
(A) 30%, 1,800
(B) 33 1/3%, 1,600
(C) 33 1/3%, 1,800
(D) 35%, 1,500
(E) 66 2/3%, 1,600
(A) 30%, 1,800
(B) 33 1/3%, 1,600
(C) 33 1/3%, 1,800
(D) 35%, 1,500
(E) 66 2/3%, 1,600
Re: The simple interest for 10 years is Rs. 6,000. The compound interest
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08 Jun 2021, 06:34
08 Jun 2021, 06:34
The simple interest for 10 years is 6,000 means that every year the investment earns 600. The only one where is this is true is true is C. 1800/3 = 600.
1800 with 33.33333% interest compounded over 2 years yields 600 in the first year, and then in the second year yields another 600 plus 33.33333% interest on the 600 earned in the previous year, which is 200. 600+600+200 = 1400
Answer C
1800 with 33.33333% interest compounded over 2 years yields 600 in the first year, and then in the second year yields another 600 plus 33.33333% interest on the 600 earned in the previous year, which is 200. 600+600+200 = 1400
Answer C
The simple interest for 10 years is Rs. 6,000. The compound interest
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08 Jun 2021, 07:01
08 Jun 2021, 07:01
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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 %
Posted from my mobile device
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 %
Posted from my mobile device
