Question

2. You deposited money into an account that pays 3.425% interest

compounded continuously. How long will it take for your money to
double? Write an equation to represent the situation. Round to the
nearest hundredths if necessary.

Answer 1

t=20.24 years

Explanation:

-Continuous compounding happens over an infinite number of periods and is given by the formula:

`A=Pe^(rt)`

Where:

• 
  `A` is the future value of the investment
• 
  `P` is the principal amount invested
• 
  `r,\ t` is the rate of interest and time respectively.

#We substitute the given values in the equation to solve for t:

`A=2P\\\\\therefore 2P=Pe^(rt)\\\\2=e^(0.03425t)\\\\t=(In \ 2)/(0.03425)\\\\=20.237874\approx20.24\ years`

Hence, it takes approximately 20.24 years for the principal to double in value.