Find exact answer thats hard to do for part Cbut 6 is a frie

Find exact answer (that\'s hard to do for part C-but 6% is a friendly number) and the time rounded to three decimal places. 3) Calculating t: Assume r = 6%. How long will it take to double your principle under each of the following conditions? A) NOT compounded. B) Compounded annually C) Compounded quarterly D) Compounded monthly E) Compounded continuously

Solution

3)

r=6% =0.06

(a)

A=2P

A=P(1+rt)

(1+0.06t)=2

=>0.06t=1

=>t=1_/0.06

=>t=16.667 years

it takes 16.667 years

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(b)

A=2P

A=P(1+ r_/n)^nt

(1+0.06)^t=2

=>1.06^t=2

=>t=(ln2)_/(ln1.06)

=>t=11.896 years

it takes 11.896 years

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(c)

A=2P

A=P(1+ r_/n)^nt,n=4

(1+(0.06_/4))^4t=2

=>1.015^4t=2

=>t=(1_/4)(ln2)_/(ln1.015)

=>t=11.639 years

it takes 11.639 years

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(d)

A=2P

A=P(1+ r_/n)^nt,n=12

(1+(0.06_/12))^12t=2

=>1.005^12t=2

=>t=(1_/12)(ln2)_/(ln1.005)

=>t=11.581 years

it takes 11.581 years

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(e)

A=2P

A=Pe^rt

e^0.06t =2

=>0.06t =ln2

=>t=(1_/0.06)ln2

=>t=11.552 years