Need help with word problem please

Question

If Tanisha has $100 to invest at 9% per annum compounded semianually, how long will it be before she has $200? Also, if the compounding is continuous, how long will it be?

Answer 1

We have a nice little formula to solve this!

A = P[ 1 + (r/n) ]^(n*t)

where

P = The principle (The initial amount you borrow or deposit)

r = The annual rate of interest (The percentage)

t = The number of years the amount is deposited or borrowed

n = The number of times the interest is compounded per year

A = The amount after time t

For the first part of this problem, we have:

P = 100

r = 9% --> 0.09

n = semiannually --> 2

A = 200

Plugging those in we get:

$200 = $100[ 1 + (0.09/2) ]^(2*t)

All that's left is to solve for t! For continuous compounding, we use the same method but a slightly different formula:

A = P*e^(r*t)

Hope this helps!

Answer 2

2 = (1 + 0.09/2)^2t

2 = 1.045^2t

ln 2 = ln 1.045 (2t)

Can you solve for t and answer?

2 = e^0.09t

ln 2 = 0.09t

Can you solve for t and answer?