Compound Interest
 Let Principal = P, Rate = R% per annum, Time = n
 When interest is compound Annually:
Amount = P  1 +  R  n  
100 
 When interest is compounded Halfyearly:
Amount = P  1 +  (R/2)  2n  
100 
 When interest is compounded Quarterly:
Amount = P  1 +  (R/4)  4n  
100 
 When interest is compounded Annually but time is in fraction, say 3
Amount = P  1 +  R  3  x  1 +  R  
100  100 
 When Rates are different for different years, say R_{1}%, R_{2}%, R_{3}% for 1^{st}, 2^{nd}and 3^{rd} year respectively.
Then, Amount = P  1 +  R_{1}  1 +  R_{2}  1 +  R_{3}  .  
100  100  100 
 Present worth of Rs. xdue n years hence is given by:
Present Worth =  x  .  

Questions:
LevelI:
1.  A bank offers 5% compound interest calculated on halfyearly basis. A customer deposits Rs. 1600 each on 1^{st}January and 1^{st} July of a year. At the end of the year, the amount he would have gained by way of interest is:  

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:  

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?  

4.  What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and halfyearly?  

5.  The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:  


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.?  

7.  At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?  

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:  

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?  

10.  The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable halfyearly is:  


11. 
LevelII:
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: 


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?  

13.  The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned halfyearly is:  

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?  

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:  


16. 



17. 



18. 



Answers:
LevelI:
Answer:1 Option B
Explanation:
Amount 








= Rs. 3321. 
 I. = Rs. (3321 – 3200) = Rs. 121
Answer:2 Option A
Explanation:
Let the sum be Rs. x. Then,
C.I. =  x  1 +  4  2  – x  =  676  x  – x  =  51  x.  
100  625  625 
S.I. =  x x 4 x 2  =  2x  .  
100  25 
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 =  100 x 60  = 10% p.a.  
100 x 6 
Now, P = Rs. 12000. T = 3 years and R = 10% p.a.
C.I. 




= 3972. 
Answer:4 Option A
Explanation:
C.I. when interest compounded yearly 




= Rs. 5304. 
C.I. when interest is compounded halfyearly 




= 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  1 +  7  n  = 34347  
100 
107  n  =  34347  =  11449  =  107  2  
100  30000  10000  100 
n = 2 years.
Answer:6 Option C
Explanation:
Amount 




= 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  1 +  R  2  = 1348.32  
100 
1 +  R  2  =  134832  =  11236  
100  120000  10000 
1 +  R  2  =  106  2  
100  100 
1 +  R  =  106 
100  100 
R = 6%
Answer:8 Option B
Explanation:
P  1 +  20  n  > 2P  6  n  > 2.  
100  5 
Now,  6  x  6  x  6  x  6  > 2.  
5  5  5  5 
So, n = 4 years.
Answer:9 Option C
Explanation:
Amount 




= Rs. 8820. 
Answer:10 Option D
Explanation:
Amount of Rs. 100 for 1 year when compounded halfyearly 
= Rs.  100 x  1 +  3  2  = Rs. 106.09  
100 
Effective rate = (106.09 – 100)% = 6.09%
Answer:11 Option C
Explanation:
C.I. 




= Rs. 840. 
Sum = Rs.  420 x 100  = Rs. 1750.  
3 x 8 
Answer:12 Option A
Explanation:
Sum = Rs.  50 x 100  = Rs. 500.  
2 x 5 
Amount 




= Rs. 551.25 
 I. = Rs. (551.25 – 500) = Rs. 51.25
Answer:13 Option B
Explanation:
S.I. = Rs  1200 x 10 x 1  = Rs. 120.  
100 
C.I. = Rs.  1200 x  1 +  5  2  – 1200  = Rs. 123.  
100 
Difference = Rs. (123 – 120) = Rs. 3.
Answer:14 Option A
Explanation:
15000 x  1 +  R  2  – 15000  –  15000 x R x 2  = 96  
100  100 
15000  1 +  R  2  – 1 –  2R  = 96  
100  100 
15000  (100 + R)^{2} – 10000 – (200 x R)  = 96  
10000 
R^{2} =  96 x 2  = 64  
3 
R = 8.
Rate = 8%.
Answer:15 Option B
Explanation:
Let the sum be Rs. P.
Then,  P  1 +  10  2  – P  = 525  
100 
P  11  2  – 1  = 525  
10 
P =  525 x 100  = 2500.  
21 
Sum = Rs . 2500.
So, S.I. = Rs.  2500 x 5 x 4  = Rs. 500  
100 
Answer:16 Option D
Explanation:
Let Principal = Rs. P and Rate = R% p.a. Then,
Amount = Rs.  P  1 +  R  4  
100 
C.I. =  P  1 +  R  4  – 1  
100 
P  1 +  R  4  – 1  = 1491.  
100 
Clearly, it does not give the answer.
Correct answer is (D).
Answer:17 Option C
Explanation:
I. Amount = Rs.  200 x  1 +  6  16  
100 
II. Amount = Rs.  200 x  1 +  6  16  
100 
Thus, I as well as II gives the answer.
Correct answer is (C).
Answer:18 Option E
Explanation:
Given: T = 3 years.
 gives: R = 8% p.a.
 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).