Question

How many years will the following take?
$300 to grow to $34,405 if invested at 12.12 percent, compounded annually.

Round the answer to two decimal places.

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.

34,405=300*(1.1212)^n

(34,405/300)=(1.1212)^n

Taking log on both sides;

log (34,405/300)=n*log (1.1212)

n=log (34,405/300)/log (1.1212)

=41.45 years(Approx).

Answer 2

SOLUTION :

Let n years be be taken for $300 to grow to $34405 , invested at 12.12 %  compounded annually.

Rate, r = 12.12 % = 0.1212

So, 

FV = PV( 1+ r)^n

=> 34405 = 300(1 + 0.1212)^n

=> (1 + 0.1212)^n = 34405/300

Taking log :

=> n log(1.1212) = log(34405/300)

=> n = log(34405/300) / log(1.1212)

=> n = 41.45  years approx. 

41.45  years will be taken for $300 to grow to $34405 , invested at 12.12 %  compounded annually.  (ANSWER)