SOLUTION: 4) How long will it take a sum of money to double at 5% per annum compounded continuously? a) 5 years b) 13.9 years c) 16.4 years d)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 4) How long will it take a sum of money to double at 5% per annum compounded continuously? a) 5 years b) 13.9 years c) 16.4 years d)       Log On


   

Question 121739: 4) How long will it take a sum of money to double at 5% per annum compounded continuously?

a) 5 years
b) 13.9 years
c) 16.4 years
d) 19.1 years
e) 12.5 years
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember the formula for compounding interest continuously is


A=Pe%5E%28rt%29 where A is the return, P is the principal, r is the interest rate and t is the time


So if we want to know when our money will double, this means that A will be twice as much as P. In other words, A=2P


A=Pe%5E%28rt%29 Start with the given formula


2P=Pe%5E%280.05t%29 Plug in A=2P and r=0.05 note: 5% is the decimal number 0.05


2P%2FP=e%5E%280.05t%29 Divide both sides by P


2=e%5E%280.05t%29 Divide


ln%282%29=0.05t Take the natural log of both sides. This will eliminate the base "e"



ln%282%29%2F0.05=t Divide both sides by 0.05 to isolate t



0.69315%2F0.05=t Use a calculator to evaluate ln%282%29. Note: ln%282%29=0.69315


13.863=t Divide



Now if you round to the nearest hundredth, the answer is:


t=13.9

So it will take about 13.9 years to double any given sum of money


So the answer is B)