Question

 How many years will it take for ​$490 to grow to ​$1,026.32 if​ it's invested at 6 percent compounded​ annually? The number of years it will take for ​$490 to grow to ​$1,026.32 at 6 percent compounded annually is (Round to one decimal​ place.)

Answer 1

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

1,026.32=490*(1.06)^n

(1,026.32/490)=(1.06)^n

Taking log on both sides;

log (1,026.32/490)=n*log 1.06

n=log (1,026.32/490)/log 1.06

=12.7 years(Approx).

Answer 2

SOLUTION :

Let n years be be taken for $490 to grow to $1026.32 , invested at 6%  compounded annually.

Rate, r = 6% = 0.06

So, 

FV = PV( 1+ r)^n

=> 1026.32 = 490(1 + 0.06)^n

=> (1 + 0.06)^n = 1026.32/490

Taking log :

=> n log(1.06) = log(1026.32/490)

=> n = log(1026.32/490) / log(1.06)

=> n = 12.7 years approx.

12.7 years will be taken for $490 to grow to $1026.32 , invested at 6%  compounded annually.  (ANSWER)