How long would it take an investment of $6000 to amount to $9000 if interest is earned at 7% compounded continuously ?.
1. Ask yourself what you want to find ? - You want to find time ( how long it would take )
2.Clue in question - Continuous compounding
3.Use formula FV=PV.e(r.t)
Where FV=Future Value, PV=present value, e=exponent (ln) , r=rate expressed as a decimal , t=time in years
4.Plugging in the information given
9'000=6000.e(.07.t)
9'000/6000=e(.07t)
1.5=e(.07t)
Taking ln
ln(1.5)=lne (lne=1)(.07t)
using scientific cal(ln1.5).40546=1(.07t)
.40546/.07=t
5.8=t
5.8 years or 5 years 9 months and 18 days
correct , small point .....
after 1.5 = e^(.07t)
ln 1.5 = .07 lne
.07t = ln 1.5 , since lne = 1
t = ln 1.5/.07
= 5.79....
don't put (lne=1) as part of your solution line,
To find out how long it would take for an investment to amount to $9000 with continuous compounding at an interest rate of 7%, we can use the continuous compound interest formula:
A = P * e^(rt)
Where:
A = the final amount ($9000)
P = the initial principal ($6000)
e = Euler's number (approximately 2.71828)
r = interest rate (7% or 0.07)
t = time (unknown)
Now let's rearrange the formula to isolate the variable t:
A = P * e^(rt)
9000 = 6000 * e^(0.07t)
Divide both sides by 6000:
9000/6000 = e^(0.07t)
Simplify:
3/2 = e^(0.07t)
Take the natural logarithm (ln) of both sides to eliminate the exponential:
ln(3/2) = 0.07t * ln(e)
Since ln(e) is equal to 1, we can simplify the equation further:
ln(3/2) = 0.07t
Now we can divide both sides by 0.07:
ln(3/2) / 0.07 = t
Using a calculator, we can find the approximate value of ln(3/2) / 0.07, which is approximately 6.21.
Therefore, it would take approximately 6.21 years for the investment to grow from $6000 to $9000 if interest is earned at 7% compounded continuously.