Answer:
13.6 years
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.