Question

Find the missing values assuming continuously compounded interest. (Round your answers to two decimal places.)

Initial Investment: $100

Annual % Rate: ?

Amount of time it takes to double: ?

Amount after 10 years: $1405

Answer 1

Annual % Rate: 26.43%

Amount of time it takes to double: 2.62yr

Explanation:

Solving for r(Annual%Rate)

A=P⋅e^(r⋅t)

1405=100⋅^(r⋅10)

1405=100⋅e(^10r)

1405/100=100/100⋅e^(10r)

14.05 = e^(10r)

log(14.05) = log(e^10r)

1.1476 = 10r⋅log(e)

1.1476/log(e) = 10r

1.1476/10⋅log(e) = r

r = 0.26426

=26.43%

Now we have r=26.43%. We can use this information to solve for t, the time period to double the initial investment:

2P = Pe^(rt)

2 = e^(0.2643t)

ln(2) = 0.2643t

t = ln(2)/0.2643

t = 2.62yr