Question

Jackson invested $4,200 in an account paying an interest rate of 9 1/2 compounded continuously. Julia invested $4,200 in an account paying an interest rate of 8 7/8 compounded quarterly. To the nearest hundredth of a year, how much longer would it take for Julia's money to double than for Jackson's money to double?

Answer 1

It would Julia 0.60 years more to double the initial investment.

What is future value?

Future value means the initial investment multiplied by 2 since the future value is meant to double.

The formula for future value of a continuously interest rate is provided below:

FV=PV*e^(rt)

FV=future value=$4,200*2=$8,400

PV=initial investment=$4,200

e=exponential constant=2.7182818

r=interest rate=9.5%

t=number of years it takes for the investment to double=unknown

$8,400=$4,200*2.7182818^(9.5%*t)

$8,400/$4,200=2.7182818^(0.095t)

2=2.7182818^0.095t

take log of both sides

ln(2)=0.095t* ln(2.7182818)

0.095t=ln(2)/ln(2.7182818)

0.095t=0.69314718781684800

t=0.69314718781684800/0.095

t=7.30 years

The future value when interest is compounded quarterly is shown thus:

FV=PV*(1+r/4)^(N*4)

FV=$8,400

PV=$4,200

r=8 7/8%

r=8.875%

N=the number of years it would take for the initial investment to double=unknown

$8,400=$4,200*(1+8.875%/4)^(N4)

$8,400=$4,200*(1+0.0221875)^(N4)

$8,400/$4,200=(1+0.0221875)^(N4)

2=(1+0.0221875)^(N4)

2=(1.0221875)^(N4)

take log of both sides

ln(2)=N4*ln(1.0221875)

N4=ln(2)/ln(1.0221875)

N4=31.5857423180125

N=31.5857423180125/4

N=7.90

Difference in years=7.90-7.30

difference in years=0.60 years

Find more on continuously compounded interest formula below:

brainly.com/question/3932907

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