Posted by **Anonymous** on Saturday, August 28, 2010 at 7:02pm.

Find the amount of time required to double a dollar investment at 7.72%, if the interest is compounded continuously.

4.49 years

8.98 years

17.96 years

I'm not understanding this, I got 3.9 years when I tried to solve this.

- PreCalc -
**MathMate**, Saturday, August 28, 2010 at 7:32pm
The basic formula for compounding continuously is:

Lim (1+r/n)^(nt)

as n→∞

where t=number of years, and r is the annual interest rate.

which results in the formula:

A(t)=A(0)e^(rt)

For doubling,

A(t)/A(0)=2

Therefore:

e^(0.0772t) = 2

Take natural log on both sides to get:

0.0772t = ln(2)

Solve for t.

- PreCalc -
**Reiny**, Saturday, August 28, 2010 at 7:35pm
continuous compounding formula is

amount = principal(e^(it)) , so

2 = 1(e^.0772t)

ln2 = ln (e^.0772t)

.0772 lne = ln2 , but ln e = 1

t = ln2/.0772 = 8.98

how did you get 3.9 ?

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