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
A=P(1+r)^t
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

t= log2/log1.078=9.22 years
But
0.22cancel([year])*((12[months])/(1cancel([year])))=2.64[months] => 3[months]
So
t=9 years and 3 months