Question

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?

Answer 1

#$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