# What is the balance if $20,000 is invested at an annual rate of 7.8 percent for 5 years, compounded continuously. How long will it take for the original amount to double in size?

##### 1 Answer

Mar 24, 2016

#$29,115.46. It will take 9.22 years (9 years and 3 months) to double the originally invested capital

#### Explanation:

Using the formula

where

A - final amount

P - principal or originally invested capital

r - interest rate (per year, per month, per day)

t - time

First question

#A=20,000(1+0.078)^5#

#A=20,000*1.078^5=$29,115.46#

Second question

#2cancelP=cancelP(1+r)^t#

#log(2) = log(1.078) *t#

But

So