Simple and Compound Interest

1.  Mohan borrowed some money at the rate of 5 % p. a. for the first two years, at a rate of 8 % p. a for the next three years, and at the rate of 10 % for the period beyond five years.. If he pays total interest of Rs. 12500 at the end of 8 years, how much mony did he borrows ? 

Solution:
Let P be the sum borrowed
[ (P x 5 x 2)/100 ] + [ (P x 8 x 3)/100 ] +[ (P x 10 x 3)/100 ] 
=12500,
P=19531.25

2.  A sum of money doubles itself in 8 years at simple interest. What is the rate of interest ? 

Solution:
Let sum = x then Simple Interest = x

Rate = (100 * x) / (x * 8) = 12.5

3.  A sum of money amounts to Rs. 9800 after 5 yers and Rs. 12005 after 8 years at the same rate of simple interest. What is the rate of interest per annum ?

Solution:
We can get SI of 3 years = 12005 - 9800 = 2205
SI for 5 years = (2205/3)*5 = 3675 [so that we can get principal amount after deducting SI]
Principal = 12005 - 3675 = 6125 
So Rate = (100*3675)/(6125*5) = 12%

4. A sum of money doules itself at compound interest in 15 years. In how many years will it become eight times ? 

Solution:
2P=p(1+r/100)^15
(1+r/100)=2^(1/15)
so
8p=p(1+r/100)^T
2^3=2^(T/15)
so T=45yrs

5. 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 ? 

Solution:
P(R / 100)^2 
=>15000( R^2/10000)=96
3(R^2 / 2) =96
R^2=64
R=8

6.  A sum of money is lent out at compound interest rate of 20 % per annum for two years. It would fetch Rs. 482 more if interest is compounded half-yearly. Find the sum 

Solution:

Let sum=Rs.x

C.I. when compounded half yearly = 

C.I. when compounded annually =

=> x=20000

7. A certain sum of money at simple interest becomes Rs. 1062 in 2 years and Rs. 1183.50 in 3½ years. What is rate of interest per annum? 
a) 7%
b) 6% 
c) 9% 
d) 5% 

Solution:

8. If the simple interest on a sum at 4% per annum for 2 years is Rs. 80, then the compound interest on the same sum for the same period is: 
a) Rs. 86.80 
b) Rs. 86.10
c)Rs. 88.65 
d) Rs. 81.60 

Solution:
Amount from simple interest is 1000.then calculate the amount from this formula
a=p(1+r/100)^n.
so,1000(1+4/100)^2 =1081.6.
so, interest is 81.6

9. A committee is to be formed comprising 7 members such that there is a simple majority of men and at least 1 women. The shortlist consists of 9 men and 6 women. In how many ways can this be done? 
a) 3,724 
b) 3,630 
c) 4,914 
d) 5,670 

Solution:
committee of seven members 
we have possibility of atleast one female and not more than the male .we have 9 male and 6 female

9c6*6c1+9c5*6c2+9c4*6c3
=84*6+126*15+126*20
=4914

10. Consider the following statements : If a sum of money is lent at simple interest, then the  1. Money gets doubled in 5 years if the rate of interest is 50/3 %. 2. Money gets doubled in 5 years if the rate of interest is 20%. 3. Money becomes 
a) 1 and 3 are correct 
b) 2 alone is correct- 
c) 3 alone is correct 
d) 2 and 3 are correct 

Solution:

2 alone is correct

11. The difference between simple interest and compound interest on Rs.1200 for one year at 10% per annum reckoned half-yearly is: 

a) Rs. 2.50 

b) Rs. 3  

c)Rs. 3.75 

d) Rs. 4

Solution:

S.I = PRT/100
= (1200*10*1)/100=120

Now,( { Half yearly C.I. } - 1200 )

C.I.= [{P(1+R/2/100)^2N}-1200] 

= [ {1200(1+5/100)^2= 1323 } -1200 ]
=123

difference = 123-120 = 3

12. The simple interest on Rs. 10 for 4 months at the rate of 3 paise per rupee per month is: 
a) Rs. 1.20 SI
b) Rs. 1.60 
c) Rs. 2.40 
d) Rs. 3.60 

Solution:
 =(10 * 3/4 * 4) =Rs. 1.20 

13. If the compound interest on a sum for 2 years at 25/2 % per annum is Rs. 510, the simple interest on the same sum at the same rate for the same period of time is: 
a) Rs. 400 
b) Rs. 450 
c) Rs. 460 
d) Rs. 480 

Solution:
Rs. 480

14. In a town the population grows at a simple rate of 10% in a decade and compounds from decade to decade. Find the population at the beginning of the 1970s if the population at the beginning of the 1990s is 3,63,000 people. 
a) 30,000 
b) 3,00,000 
c) 30,00,000 
d) 3,15,000

Solution: 
3,63,000/1.1*1.1= 3,00,000
because increase by 10% thats by multiply by 1.1

15. In approximately how many years will a certain sum of money triple itself at 22% simple interest? 
a) 10 years 
b) 11 years 
c) 9 years 
d) 12 years 

Solution:
100 / 11 = 9  years (approx)