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:
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