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- Most Important Multiple Choice Questions
- Online Exercise on Interest with Correct Answer Key and Solutions
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Question 1 of 18
1. Question
What annual payment will discharge a debt of Rs 50,440 due in 3 years at 5% per annum compounded annually?
Hint
Let each installment be Rs x. Then,
(Present worth of Rs x due 1 year hence) + Present worth of Rs x due 2 years hence) + (Present worth of Rs x due 3 years hence) = 50440
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Question 2 of 18
2. Question
A sum of money yields at compound interest Rs 200 and Rs 220 at the end of first and second year respectively. The rate % is
Hint
Let Principal P = Rs x, R = r%,
C.I. = 200 at the end of Ist year
or 200 + 220 at the end of IInd year
We know that
At the end of Ist year
…(1)At the end of 2nd year
…(2)On dividing (2) by (1) we get
⇒
⇒ r = 0.10 × 100
⇒ r = 10%
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Question 3 of 18
3. Question
The compound interest accrued on an amount of Rs 25,500 at the end of three year is Rs 8,440.5. What would be the simple interest accrued on the same amount at the same rate in the same period?
Hint
25500
– 25500 = 8440.5 ⇒
= 8440.5 + 25500
⇒
=
⇒
⇒
⇒
∴ Simple interest
=
= Rs 7650
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Question 4 of 18
4. Question
The simple interest obtained on an amount of Rs 45,000 at the end of 4 year is Rs 15,300. What would be the approximate compound interest obtained on the same amount at the same rate of interest in the same period?
Hint
Rate =
= 8.5%
Compound interest
=
– 45000=
= 45000 × 0.3858 = Rs 17364 (approx)
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Question 5 of 18
5. Question
Parameshwaran invested an amount of Rs 12,000 at the simple interest rate of 10 pcpa and another amount at the simple interest rate of 20 pcpa. The total interest earned at the end of one year on the total amount invested became 14 pcpa. Find the total amount invested.
Hint
Let the second amount be Rs x. Then,
⇒ 120000 + 20 x = (12000 + x) 14
⇒ 6x = 168000 – 120000
⇒ x = Rs 8000
∴ Total investment
= 12,000 + 8000 = Rs 20,000
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Question 6 of 18
6. Question
Find the difference between S.I and C.I on Rs 2,000 for 2 years at the rate of 10% p.a.
Hint
For, T = 2 years
Required difference
= Rs 20
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Question 7 of 18
7. Question
The compound interest on a certain sum for 2 years is Rs 41 and the simple interest is Rs 40. Find the rate % p.a.
Hint
For T = 2 years,
C. I. – S. I.
= Rs [21600 – (2880 + 2400 + 2000)]
= Rs 14320.
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Question 8 of 18
8. Question
What would be the simple interest, if the compound interest on the same sum for 2 years at 4% be Rs 408.
Hint
For T = 2 years,
C. I. – S. I.
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Question 9 of 18
9. Question
The difference between compound interest and simple interest on a sum for 2 years at 10% per annum, when the interest is compounded annually is Rs 16. If the interest were compounded half-yearly, the difference in two interests would be:
Hint
For first year, S.I. = C.I.
Now, Rs 10 is S.I. on Rs 100.
So, S.I. on principal for 1 year at 10% is Rs 160
Amount for 2 years compounded half yearly
=
∴ C.I. = Rs (1944.81 – 1600) = Rs 24.81.
S.I. =
∴ (C.I.) – (S.I.) = Rs (344.81 – 320) = Rs 24.81.
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Question 10 of 18
10. Question
A person lent out a certain sum on simple interest and the same sum on compound interest at certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25 : 8. The rate of interest per annum is:
Hint
Let the principal be Rs P and rate of interest be R% per annum.
Differecne of C.I. and S.I. for 3 years
Difference of C.I. and S.I. for 2 years
=
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Question 11 of 18
11. Question
Rahul borrowed a certain sum from Dhawan at a certain rate of simple interest for 2 years. He lent this sum to Ramesh at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs 4200 as compound interest but paid Rs 4000 only as simple interest. Find the rate of interest.
Hint
Let the money borrowed be Rs x and the rate of interest charged = r%
Time = 2 years,
Now, 4000 =
⇒ r x = 200000 … (i)
Again,
⇒
⇒ 20r + 4000 = 4200 [from (i)]
⇒ r = 10%
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Question 12 of 18
12. Question
A person has taken a loan amount at the rate of 10 % annual compound interest and he pays that amount in two installments of Rs 968 each. How much loan did he take?
Hint
Required amount
=
=
= Rs 1680 -
Question 13 of 18
13. Question
A tree increases annually by ⅛th of its height. By how much will it increase after 2½ yearly, if it stands today 10ft high?
Hint
Increment
∴ Increment in height = 13.44 – 10 = 3.44 ft
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Question 14 of 18
14. Question
A man borrows Rs 2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 years in two equal yearly installments. How much will each installment be?
Hint
Let the value of each installment be Rs x. Then,
(present worth of Rs x due 1 year hence) + (present worth of Rs x due 2 years hence) = Rs 2550
∴ value of each installment = Rs 1352.
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Question 15 of 18
15. Question
Two friends A and B jointly lent out Rs 81,600 at 4% per annum compound interest. After 2 years A gets the same amount as B gets after 3 years. The investment made by B was
Hint
Let A lent Rs x and B lent Rs y
Since, A and B together lent out Rs 81600
∴ x + y = 81,600
Now, given (r) Rate = 4%
∴
According to the question, we have
∴ Investment made by B
=
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Question 16 of 18
16. Question
The population of a village is 10,000. If the population increases by 10% in the first year, by 20% in the second year and due to mass exodus, it decreases by 5 % in the third year, what will be its population after 3 years?
Hint
Population after 1st year
=
= 11000Population after 2nd year
=
Population after 3rd year
=
Hence, population after 3rd year = 12,540.
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Question 17 of 18
17. Question
A sum of money is accumulating at compound interest at a certain rate of interest. If simple interest instead of compound were reckoned, the interest for the first two years would be diminished by Rs 20 and that for the first three years, by Rs 61. Find the sum.
Hint
Let
and I₂ = P (1+ i)t – P = P[(1+ i)t – 1]
According to the question,
20 = P [(1 + i)² – 1–2i]
and 61 = P [(1+ i)³ – 1– 3i]
On dividing, we get
As we know,
Hence,
20×20×20 = 8000. -
Question 18 of 18
18. Question
A sum of money is put at compound interest for 2 years at 20% p.a. It would fetch Rs 482 more, if the interest were payable half-yearly, than if it were payable yearly. Find the sum.
Hint
Let sum be Rs P. Then,
… (i)and
∴ By (i),
