Question

  How many years will it take for ​$480 to grow to ​$1,020.16 if​ it's invested at 7 percent compounded​ annually? The number of years it will take for ​$480 to grow to ​$1,020.16 at 7 percent compounded annually is____  years. ​ (Round to one decimal​ place.)

Answer 1

If the amount is compounded annually,

$1,020.16 = $480/ (1.07)^n

2.12533333 = (1.07)^n

We can use the trail and error method to find n or the BA 2 plus financial calculator. Please press the following keys on your calculator-

2ND FV

1020.16 FV

-480 PV

7 I/Y

0 PMT

CPT N

N= 11.1 years

Do let me know in the comment section in case of any doubt.

Answer 2

SOLUTION :

Let n years be be taken for $480 to grow to $1020.16 , invested at 7%  compounded annually.

Rate, r = 7% = 0.07

So, 

FV = PV( 1+ r)^n

=> 1020.16 = 480(1 + 0.07)^n

=> (1 + 0.07)^n = 1020.16/480

Taking log :

=> n log(1.07) = log(1020.16/480)

=> n = log(1020.16/480) / log(1.07)

=> n = 11.1 years approx. 

11.1 years will be taken for $480 to grow to $1020.16 , invested at 7%  compounded annually.  (ANSWER)