inventment compounded continuously problem?

Question

how long will it take for an investment to double in value if it earns 7.75% compounded continuously?

that means r=.07
you use some form of the equation
A=Pe^rt i think

Answer 1

Correct:
2P = P e^(0.0775t)
2 = e^(0.0775t)
ln2 / 0.0775 = t = 8.94 years

Answer 2

Netflix consumer guy: $sixteen,000 x 4 = $sixty 4,000 (no longer $40 8,000) I agree in part with the 1st answer. however the venture is that no-one pays for 4 years of faculty up front. normally you pay for 365 days a million, then a 365 days later you pay for the subsequent 365 days, etc. So the stability after 18 years: A=(15000)e^(0.084*18)= $sixty 8,036.ninety Now procuring the 1st 365 days: $sixty 8,036.ninety-$sixteen,000 leaves $fifty two,036.ninety to nevertheless make investments. Now retaining that invested for the subsequent 365 days: A=52036.90e^(0.084*a million)= $fifty six,596.80 4. procuring 365 days 2 of faculty: $fifty six,596.80 4-$sixteen,000 leaves $40,596.80 4. making an investment that for the subsequent 365 days: 40596.84e^(0.084*a million)= $40 4,154.29. procuring 365 days 3 of faculty: $40 4,154.29-$sixteen,000 leaves $28,154.29. making an investment that for the subsequent 365 days: $28,154.29e^(0.084*a million)= $30,621.40 two. procuring 365 days 4 of faculty: $30,621.40 two-$sixteen,000 leaves $14,621.40 two. this may be slightly extra complicated then your venture states, yet this is rather how human beings do it (or pay each semester up front, yet your venture did no longer point out semesters). an exciting question is: how plenty pastime value is needed to easily pay off college (make the stability $sixteen,000 on the time of the ideal charge). the respond (making use of Excel) is 7.457982%.

Answer 3

2P = Pe^.0775t
2 = e^1.0775t
ln(2) = tln(1.0775)
t = ln(2)/ln(1.0775) = 9.29 years

The rule of 72 says time to double is 72/rate
= 72/7.75 = 9.29
I'd say the rule of 72 works pretty good.

Answer 4

2=(1.0775)^y or (years)
y is 9.something which rounds up to 10 years.