Paisley invested $3,000 in an account paying an interest rate of 3% compounded
continuously. Maya invested $3,000 in an account paying an interest rate of 4%
compounded daily. To the nearest hundredth of a year, how much longer would it
take for Paisley's money to triple than for Maya's money to triple?

9.15 years

Step-by-step explanation:

step 1

Paisley

we know that

The formula to calculate continuously compounded interest is equal to

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

substitute in the formula above

solve for t

apply ln both sides

solve for t

step 2

Maya

we know that    

The compound interest formula is equal to  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

substitute in the formula above

solve for t

Apply log both sides

step 3

we know that

To find out how much longer would it  take for Paisley's money to triple than for Maya's money to triple find the difference in years