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)

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) (Show Source): You can put this solution on YOUR website!
Remember the formula for compounding interest continuously is

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,

Start with the given formula

Plug in and note: 5% is the decimal number 0.05

Divide both sides by P

Divide

Take the natural log of both sides. This will eliminate the base "e"

Divide both sides by 0.05 to isolate t

Use a calculator to evaluate . Note:

Divide

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

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

So the answer is B)
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