If Mr kuber had lent $10 million at an interest rate of 40% p.a.to a less preferred customer Mr Narada, after how many years would the principal double itself if compounded half-yearly?
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20=10(1+40/200)2n
n is the number of years.
This reduces to finding n when (1.2)2n=2.
Now we need to use a bit of approximation here.
This is where you speed of calculation can come in handy.
(1.2)2 = 1.44
(1.2)4 =(1.44)2
Estimating (1.44)2 gives us the idea that it must lie between (1.44)2 =1.96 and (1.5)2 = 2.25.
A linera interpolation will tell us that it must be somewhere in the middle, ie around 2.10
so (1.2)4 = 2.1
hence the principal would double in slightly less that 2 years.
How to solve this?