Question

How do I solve this ?

Answer 1

Answer:

13.6 years

Step-by-step explanation:

Let Ao be the initial value.  We're interested in finding out how long it will take for A to double in value, that is, become equal to 2Ao.

We get:

2Ao = Ao(1 + 0.05/12)^(12t)

and must solve this for t.

Dividing both sides by Ao yields 2 = 1(1 + 0.05/12)^(12t), or

                                                       2 = (1 + 0.00427)^(12t)

Solve for t by taking the common log of both sides:

log 2 = 12t·log (1.00427), or

0.30103 = 12·t·0.00185.  Performing the multiplication on the right side, we get

0.30103 = 0.0222t.

Dividing both sides by 0.0222, we get:

     0.30103

t = --------------------  =  13.56

             0.0222

It will take this investment about 13 1/2 years to double in value.

Rounded to the nearest tenth, that'd be 13.6 years.