What is the number of years?

Question

If $5,400 is invested in an account earning 7% annual interest compounded continuously, then the number of years that it takes for the amount to grow to $10,800 is given by n=ln2/0.07. Find the number of years (to one decimal place).

Answer 1

The answer is in fact ln(2)/.07 here is a little explanation:

 

Using the equation for continuous compounding: 

 

A = Pe^RT

 

Where:

A = Amt after time T

P = Principal Invested

R = Annual interest Rate

T = Number of Years

 

We find that the number of years required for $5,400 to appreciate to $10,400 at 7% interest continually compounded is 9.9:

 

10,800 = 5,400*e^.07T

 

2=e^.07T

 

ln(2) = .07T

 

ln(2)/.07 = T

 

9.9 years = T

 

Alternatively, because the investment doubled you could have used a shortcut called the law of 69.3. This law states that an investment will double in size every X years where X is 69.3 divided by the annual interest rate:

 

69.3/7=9.9 years

 

Hope this helps.