Question

Suppose $40,000 is invested in an account that returns 7% per year compounded continuously. (Round your answers to one decimal place.)

a. how long will it take for the investment to double? ____ yrs

b. How long will it take for the investment to triple? _____ yrs

Answer 1

Given; principal=$40,000, rate=7%

a)amount=$80,000, b) $120,000

we have to find time.

Formula for calculation of compound intrest

A=P(1+r/n)n*t where

a). A= amount + $80,000

P=principal =$40,000

r= intrest rate in decimal=0.07

n= number of times intrest is componded per unit time= 1

t= time in years

put all these values in above formula

$80,000=$40,000(1+0.07)t

2=1.07t

take ln on both side

ln(2)=t ln(1.07)

t=ln(2)/ln(1.07)= 10.25 years.

B) amount=$120,000

$120,000=$40,000(1+0.07)t

3=(1+0.07)t

take ln on both side

ln(3)=ln(1.07)*t

t=ln(3)/ln(1.07)=16.237 years