Question

 How many years will it take for

$500

to grow to

$1,039.50

if it's invested at

5

percent compounded annually?

The number of years it will take for

$500

to grow to

$1,039.50

at

5

percent compounded annually is

nothing

years

Answer 1

We use the formula

A=P(1+r/100)^n

Where A =future value

P is present value

R is rate of return

N=time period

1003.78=510(1.09)^n

(1003.78/510)=(1.09)^n

Taking log on both sides;

Log (1003.78/510)=n*log 1.09

n=log (1003.78/510)/log 1.09

=7.86 years(approx).

Answer 2

SOLUTION :

Let n years be be taken for $500 to grow to $1039.50 , invested at 5%  compounded annually.

Rate, r = 5% = 0.05

So, 

FV = PV( 1+ r)^n

=> 1039.50 = 500(1 + 0.05)^n

=> (1 + 0.05)^n = 1039.50/500

Taking log :

=> n log(1.05) = log(1039.50/500)

=> n = log(1039.50/500) / log(1.05)

=> n = 15 years

15 years will be taken for $500 to grow to $1039.50 , invested at 5%  compounded annually.  (ANSWER)