Albert.io Algebra 2 Question

Question

How long in years, rounded to the nearest whole year, will it take for an investment of $2000 to double in its value if the interest rate is 7.25% per year, compounded continuously?

Answer 1

The formula for continuous compounding is:

A=Pe^rt

Plugging in the values given

4000=2000e^0.0725t To solve, divide both sides by 2000

4000/2000=2000e^0.0725t /2000 Simplify

2=e^0.0725t take the ln of both sides

ln(2)=(0.0725t) ln(e) Simplify (ln(e)=1)

ln(2)=0.0725t divide both sides by 0.0725

ln(2)/0.0725=0.0725t/0.0725 Simplify

t=9.6 years