HOW CAN I SOLVE THE =(1.03)^6

Question

I WANT TO KNOW HOW  CAN I SOLVE THE= 5000(1.03)^6 AND THE EXPLAINED ANSWER 

Answer 1

Hi Subhankar!  We can approximate ....

1.03 is a 3% gain factor happening 6 successive times, like compound interest (1.03)(1.03)(1.03)(1.03)(1.03)(1.03) on money

"rule of 72":  divide 72 by the gain factor (or interest rate) to find how may successions are needed to double the amount

for 1.03, you would need 24 successions to double -- (1.03)^24 = 2.00

12 successions would get us only half-way thru the process, or the square root of 2 = 1.4

6 successions would get us only half-way thru the process to 1.4 -- take sq. root of 1.4 = 1.2

5000 X 1.2 = 6000