Question

How long will it take for $2,000 to double if it is invested at 7% annual interest compounded 3 times a year? Enter in exact calculations or round to 3 decimal places.
It will take years to double.
How long will it take if the interest is compounded continuously?
Compounded continuously, it would only take years.

Answer 1

double ... 2 = [1 + (.07 / 3)]^(3 y) ... ln(2) = 3 y ln[1 + (.07 / 3)]
... solve for y


continuously ... 2 = e^(.07 y) ... ln(2) = .07 y

Answer 2

Compounded three times a year? How unusual, anyway ....
1(1 + .07/3)^n = 2, where n is the number of 4 month periods
1.023333...^n = 2
n log 1.023333.... = log2
n = log 2/log 1.02333.. = .... periods.

the $2000 has nothing to with the question.

for continuous compounding:
e^.07t = 2
.07t = ln 2
etc.

Answer 3

I found the answer 10.017
and the compound continuous answer is 99.02