- A city has 10,000 residents. Its population grows at the rate of 10% per annum, what’ll be its total population after 5 years?
- A bank offers 10% interest rate compounded annually, if you deposit Rs. 10,000 today, what’ll be the total amount in your savings account after 5 years?
- A butler steals 10 ml of whiskey from 100 ml bottle and replaces it with water. He repeats this process 5 more times, how much % whisky is left in the bottle?
CASE I : CITY POPULATION
A city has 10,000 residents. Its population grows at the rate of 10% per annum, what’ll be its total population after 5 years?
10% increase
=100% we have already + 10% new is added
=100%+10%
=110%
But if we talk in fraction form: 100% = 1 and 10%=1/10
Hence
10% increase
=1+1/10
=11/10
AFTER Ist YEAR:
The new population after 1 year, will be 11/10 times the original
=(11/10)*original ; we know that originally there are 10,000 resident. But no need to calculate that right now.
This is our new original:
AFTER IInd YEAR:
The new population will be 11/10 times the original population at the end of first year
=11/10*[(11/10)*original]
AFTER IIIrd YEAR:
The new population will be 11/10 times the original
=11/10 [11/10 [(11/10)*original]]
Continuing like this, what we get after 5 years is
CASE: POPULATION DECLINE
A city has 10,000 residents. Its population declines at the rate of 10% per annum, what’ll be its total population after 5 years?
Decline = decrease
=100%-10%
=1-(1/10)
=9/10
REPEAT This Step 4 more times.
EASY WAY :
COMPOUND INTEREST IS COMPOUNDED EVERY TIME. i.e YOUR INTEREST INCREASES WITH TIME IT IS VARIABLE IN NATURE WHEREAS SIMPLE INTEREST REMAINS SAME IT IS INVARIABLE. LET US HAVE A LOOK AT SIMPLE INTEREST.
SIMPLE INTEREST = (P*R*T)/100.
EXAMPLE:
QUESTION 1 - Steve invested Rs. 10,000 in a savings bank account that earned 2% simple interest. Find the interest earned if the amount was kept in the bank for 4 years.
Solution:
Principle P = Rs 10,000 Time Period T =4 years and Rate of Interest = 2% = 0.02
Plugging these values in the simple Interest formula,
I = PX T X R {here we have take R in terms of fraction so no need of dividing by 100.
= 10,000 X 4 x 0.02
= Rs. 800
Interest earned for the investment = Rs. 800.
QUESTION 2- Ryan bought Rs.15,000 from a bank to buy a car at 10% simple Interest. If he paid Rs. 9,000 as interest while clearing the loan, find the time for which the loan was given.
Solution : Principle = Rs 15,000 Rate of Interest R = 10% and the Interest paid = I = Rs. 9,000. And T is to be found.
T = (I x 100) /(PR)
= 9000/(15,000 x 0.10)
= 6 years.
The loan was given for 6 years.
So from the above 2 example we just learn about what exactly the SI is Now let us have a simplified Formula for COMPOUND INTEREST.
AMOUNT = P*(1+R/100)t
In This Formula we are having Amount not interest, For calculation of Interest,
INTEREST = AMOUNT - PRINCIPAL.
IN THE ABOVE FORMULA,
P = PRINCIPAL,
R = RATE OF INTEREST IN% per annum,
t = time period,
Now let us try to solve the Above Stated Problems,
Q.A city has 10,000 residents. Its population grows at the rate of 10% per annum, what’ll be its total population after 5 years?
A. In this case P= 10,000
R=10% per annum,
t= 5 years,
using the formula,
Population after 5 years = 10000(1+10/100)5 .
When In some questions there is an increase for 1st year and then there is decrease,In that case
A=P(1+r/100)(1-a/100)......... and so on,
Here in the above formula,
P= Principal/Initial Population,
r= Rate of increase in %,
a= Rate of Decrease in %,
SSC CGL 2016 PREPHELP
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