for the value of the investment to be doubled, it will take about t= ? years

Question

A person invest 3000$ in an account at 10% interest compounded annually. When will the value of the investment be doubled? Explain why it will take less than 10 yrs even though the rate is 10%

Answer 1

The formula for interest compounded annually is:

 

A = P(1+r)ⁿ

 

Where A is the value of the investment, P is the initial amount invested, r is the rate of return expressed as a decimal, and n is the number of years.  In your problem, we know that A = 2P, or double the initial investment.  We need to solve for n, the number of years it took to double the investment.

 

A = P(1+r)ⁿ                        

 

2P = P(1.1)ⁿ                           [A=2P, r= 0.1]

 

2 = (1.1)ⁿ                               [Divided both sides by P]

 

ln(2) = ln(1.1ⁿ) = n*ln(1.1)      [Take the natural log (ln) of both sides; ln(a^b) = b*ln(a)]

 

ln(2)/ln(1.1) = n                      [Divide both sides by ln(1.1)]

 

7.27 years = n                      [Use your calculator to compute the values of the logs]