Applications of Exponential Functions?

Question

Find the time necessary for an initial investment to double in value when placed in an account that pays 6% compounded monthly. Can you please show me the steps on how you arrived to the answer?

Thanks a bunch,
Big Bird

Answer 1

x(1+0.06)^t=2x
Divide by x on both sides.
Just so you know, x is initial amount.
1.06^t=2
log(1.06)2=t
Use the calculator.
About 12 months.

Answer 2

amt = prin(1+i)^n

since interest is compounded monthly

Let i = 0.06/12

n (number of months) is the unknown

amt/prin = 2 (since the initial investment doubled)

2 = (1+i)^n

2 = (1+0.06/12)^n

2 = (1.005)^n

Take the natural log of both sides (could use common logs)

ln 2 = (n)( ln 1.005)

n = (ln 2)/(ln 1.005)

n ≈ 139 months or 11.6 yrs
.

Answer 3

1.06^t = 2
t = ln2 / ln(1.06) = 11.89 months