the population of a country was 55 crores in 2005 and is growing at 2% p.a C.I , the population in the year 5015 is estimated as ?
a)5705
b)6005
c)6700
Shall I assume that 2% p.a C.I means
2% per annum compounded instantaneously ?
the amount = 55 e^.02t
if 2005 ---> t = 0
then 2015 --- t = 10
amount = 55 e^(.02(10))
= 67.177 crores
(is 1 crore equal to 10 million?
I see one answer as 6700, but that would not match your units.)
in the year 2015***
THANKS
The answer is none of the above
Because the exact answer is 67.17 crores.
To find the population in the year 5015, we need to apply the compound interest formula.
The compound interest formula is given by:
A = P (1 + r/n)^(nt)
Where:
A = Final amount (population in the year 5015)
P = Principal amount (population in 2005)
r = Annual growth rate (2% or 0.02 in decimal form)
n = Number of times the interest is compounded per year (assuming it is compounded annually, n = 1)
t = Number of years (5015 - 2005 = 3010)
Substituting the given values into the formula, we have:
A = 55 crores (1 + 0.02/1)^(1*3010)
Simplifying the equation:
A = 55 crores (1.02)^3010
Now, let's calculate the value using a calculator or a programming language:
A ≈ 55 crores * 108.44450436
A ≈ 6004.4497448 crores
Therefore, the estimated population in the year 5015 is approximately 6004.45 crores.
Thus, the correct option is b) 6005.