Word problem (math)

Question

Suppose $2,000 is invested in an account at annual  interest rate of 6.5% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size?

Answer 1

The formula for compound interest is A = Pe^rt where 

 

A = Accumulated or final amount

P = Principal or original amount

r = Rate as a decimal

t = time 

 

The investment will double when A = 2*P so solve 

 

2*P = Pe^0.065t

e^0.065t = 2

 

Take the natural log of both sides 

 

0.065t = ln(2)

t  ln(2)/0.065 ~ 10.7 years