Compound Interest
- Let Principal = P, Rate = R% per annum, Time = n years.
- When interest is compound Annually:
Amount = P |
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1 + |
R |
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n |
100 |
- When interest is compounded Half-yearly:
Amount = P |
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1 + |
(R/2) |
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2n |
100 |
- When interest is compounded Quarterly:
Amount = P |
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1 + |
(R/4) |
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4n |
100 |
- When interest is compounded Annually but time is in fraction, say 3 years.
Amount = P |
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1 + |
R |
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3 |
x |
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1 + |
R |
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100 |
100 |
- When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively.
Then, Amount = P |
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1 + |
R1 |
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1 + |
R2 |
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1 + |
R3 |
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100 |
100 |
100 |
- Present worth of Rs. x due n years hence is given by:
Present Worth = |
x |
. |
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Questions:
Level-I:
1. |
A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1stJanuary and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is: |
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2. |
The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is: |
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3. |
There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate? |
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4. |
What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly? |
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5. |
The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is: |
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6. |
What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.? |
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7. |
At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years? |
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8. |
The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is: |
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9. |
Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit? |
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10. |
The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is: |
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11. |
Level-II:
Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is: |
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12. |
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time? |
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13. |
The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is: |
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14. |
The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum? |
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15. |
The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is: |
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16. |
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17. |
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18. |
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Answers:
Level-I:
Answer:1 Option B
Explanation:
Amount |
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= Rs. 3321. |
- C.I. = Rs. (3321 – 3200) = Rs. 121
Answer:2 Option A
Explanation:
Let the sum be Rs. x. Then,
C.I. = |
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x |
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1 + |
4 |
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2 |
– x |
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= |
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676 |
x |
– x |
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= |
51 |
x. |
100 |
625 |
625 |
S.I. = |
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x x 4 x 2 |
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= |
2x |
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100 |
25 |
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51x |
– |
2x |
= 1 |
625 |
25 |
- x = 625.
Answer:3 Option C
Explanation:
Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = |
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100 x 60 |
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= 10% p.a. |
100 x 6 |
Now, P = Rs. 12000. T = 3 years and R = 10% p.a.
C.I. |
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= 3972. |
Answer:4 Option A
Explanation:
C.I. when interest |
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= Rs. 5304. |
C.I. when interest is |
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= Rs. 5306.04 |
Difference = Rs. (5306.04 – 5304) = Rs. 2.04
Answer:5 Option A
Explanation:
Amount = Rs. (30000 + 4347) = Rs. 34347.
Let the time be n years.
Then, 30000 |
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1 + |
7 |
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n |
= 34347 |
100 |
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107 |
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n |
= |
34347 |
= |
11449 |
= |
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107 |
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2 |
100 |
30000 |
10000 |
100 |
n = 2 years.
Answer:6 Option C
Explanation:
Amount |
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= Rs. 35123.20 |
C.I. = Rs. (35123.20 – 25000) = Rs. 10123.20
Answer:7 Option A
Explanation:
Let the rate be R% p.a.
Then, 1200 x |
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1 + |
R |
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2 |
= 1348.32 |
100 |
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1 + |
R |
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2 |
= |
134832 |
= |
11236 |
100 |
120000 |
10000 |
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1 + |
R |
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2 |
= |
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106 |
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2 |
100 |
100 |
1 + |
R |
= |
106 |
100 |
100 |
R = 6%
Answer:8 Option B
Explanation:
P |
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1 + |
20 |
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n |
> 2P |
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6 |
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n |
> 2. |
100 |
5 |
Now, |
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6 |
x |
6 |
x |
6 |
x |
6 |
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> 2. |
5 |
5 |
5 |
5 |
So, n = 4 years.
Answer:9 Option C
Explanation:
Amount |
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= Rs. 8820. |
Answer:10 Option D
Explanation:
Amount of Rs. 100 for 1 year |
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= Rs. |
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100 x |
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1 + |
3 |
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2 |
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= Rs. 106.09 |
100 |
Effective rate = (106.09 – 100)% = 6.09%
Answer:11 Option C
Explanation:
C.I. |
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= Rs. 840. |
Sum = Rs. |
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420 x 100 |
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= Rs. 1750. |
3 x 8 |
Answer:12 Option A
Explanation:
Sum = Rs. |
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50 x 100 |
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= Rs. 500. |
2 x 5 |
Amount |
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= Rs. 551.25 |
- C.I. = Rs. (551.25 – 500) = Rs. 51.25
Answer:13 Option B
Explanation:
S.I. = Rs |
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1200 x 10 x 1 |
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= Rs. 120. |
100 |
C.I. = Rs. |
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1200 x |
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1 + |
5 |
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2 |
– 1200 |
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= Rs. 123. |
100 |
Difference = Rs. (123 – 120) = Rs. 3.
Answer:14 Option A
Explanation:
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15000 x |
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1 + |
R |
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2 |
– 15000 |
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– |
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15000 x R x 2 |
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= 96 |
100 |
100 |
15000 |
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1 + |
R |
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2 |
– 1 – |
2R |
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= 96 |
100 |
100 |
15000 |
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(100 + R)2 – 10000 – (200 x R) |
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= 96 |
10000 |
R2 = |
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96 x 2 |
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= 64 |
3 |
R = 8.
Rate = 8%.
Answer:15 Option B
Explanation:
Let the sum be Rs. P.
Then, |
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P |
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1 + |
10 |
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2 |
– P |
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= 525 |
100 |
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P |
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11 |
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2 |
– 1 |
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= 525 |
10 |
P = |
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525 x 100 |
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= 2500. |
21 |
Sum = Rs . 2500.
So, S.I. = Rs. |
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2500 x 5 x 4 |
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= Rs. 500 |
100 |
Answer:16 Option D
Explanation:
Let Principal = Rs. P and Rate = R% p.a. Then,
Amount = Rs. |
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P |
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1 + |
R |
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4 |
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100 |
C.I. = |
P |
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1 + |
R |
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4 |
– 1 |
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100 |
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P |
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1 + |
R |
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4 |
– 1 |
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= 1491. |
100 |
Clearly, it does not give the answer.
Correct answer is (D).
Answer:17 Option C
Explanation:
I. Amount = Rs. |
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200 x |
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1 + |
6 |
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16 |
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100 |
II. Amount = Rs. |
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200 x |
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1 + |
6 |
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16 |
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100 |
Thus, I as well as II gives the answer.
Correct answer is (C).
Answer:18 Option E
Explanation:
Given: T = 3 years.
I. gives: R = 8% p.a.
II. gives: S.I. = Rs. 1200.
Thus, P = Rs. 5000, R = 8% p.a. and T = 3 years.
Difference between C.I. and S.I. may be obtained.
So, the correct answer is (E).