SOLUTION: I'm having wrapping my head around this one and could use your guidance please! Suppose $5,400 is invested in an account at an annual interest rate of 3.3% compounded continuous

Algebra ->  Finance -> SOLUTION: I'm having wrapping my head around this one and could use your guidance please! Suppose $5,400 is invested in an account at an annual interest rate of 3.3% compounded continuous      Log On


   

Question 1040435: I'm having wrapping my head around this one and could use your guidance please!
Suppose $5,400 is invested in an account at an annual interest rate of 3.3% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size?
Any help is greatly appreciated!

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

P = Initial amount deposited = 5400
A = final amount after t years = 2*5400 = 10800
r = interest rate in decimal form = 0.033
t = time in years = unknown

We're using this formula
A+=+P%2Ae%5E%28r%2At%29
where 'e' is a constant (e = 2.718... approx. It's similar to pi = 3.14...)


Let's use the values given above to find t


A+=+P%2Ae%5E%28r%2At%29


10800+=+5400%2Ae%5E%280.033%2At%29


10800%2F5400+=+%285400%2Ae%5E%280.033%2At%29%29%2F5400


2+=+e%5E%280.033%2At%29


e%5E%280.033%2At%29+=+2


0.033t+=+ln%282%29


t+=+ln%282%29%2F0.033


t+=+21.004460016968


It will take approximately 21.004460016968 years.


Round that to the nearest tenth to get the final answer of 21.0 years


Side note: Using the rule of 72, we'd have 72/x = 72/3.3 = 21.8181818181819 which is fairly close to what we got above. So this rule will give you a quick idea of the approximate doubling time.