How should I approach this, what formula do I use to solve and how do I solve it?
How long, to the nearest year, will it take me to become a millionaire if I invest $3000 at 9% interest compounded continuously?
Thanks
I got the wrong answer of 12 years
$3000 invested at continuous interest rate of 9% (=0.09) for 12 years yield a future value of
3000*e^(0.09*12)
=8834
If you want to be a millionaire, you'll need to wait a little longer!
3000*e^(0.09*n)=1000000
e^(0.09n)=3000/1000000=1000/3
Take natural log on both sides
0.09n=ln(1000/3)
n=ln(1000/3)/0.09=64.55
=approx. 64 years & 5 months and a half
To determine how long it will take you to become a millionaire by investing $3000 at 9% interest compounded continuously, you can use the formula for continuous compound interest:
A = P * e^(rt),
where:
A represents the amount accumulated,
P represents the principal investment amount,
e is the mathematical constant approximately equal to 2.71828,
r represents the interest rate, and
t represents the time in years.
In this scenario, you want to find out the value of t, which represents the time it takes to reach $1,000,000. We can rearrange the formula to solve for t:
t = (ln(A/P)) / r,
where ln represents the natural logarithm.
Now, let's substitute the given values into the formula and solve for t:
P = $3000,
A = $1,000,000,
r = 9% = 0.09.
Using the formula, we have:
t = (ln(1000000/3000)) / 0.09.
Now, you can use a scientific calculator or online calculator to evaluate ln(1000000/3000) and divide the result by 0.09. This will give you the time in years.
Remember to round the result to the nearest year for a more practical answer.
Note: Continuous compound interest assumes the interest is compounded infinitely often, which is an ideal scenario. In reality, compound interest is usually calculated annually, semi-annually, quarterly, or monthly.