You can put this solution on YOUR website! how long, to the nearest year, will it take an investment to triple if it is continuously compunded at 5% per year? . Continuous compounded interest formula: A = Pe^(rt) Where A is accumulated sum after t time P is initial principal r is rate or interest t is time . 3P = Pe^(.05t) Dividing both sides by P: 3 = e^(.05t) Take the ln of both sides: ln(3) = .05t ln(3)/.05 = t 22 years = t Yeilin J. asked • 12/16/201 Expert Answer
Fidel O. answered • 12/17/20 I will help you learn the intuition behind Math.
Hello, The continuous growth formula is A = Pert A is the final amount P is the principal amount or starting point r is your rate of growth [our 5.3 percent which is 5.3/100 = 0.053] t is time We are looking for time in this case. Well we know what A is. It is three times the value of P. A = 3P The formula then changes to 3P = Pe0.053t P is 1 so we can leave it out and just say 3 = e0.053t We take the natural log (ln) of both sides Ln(3) = Ln( e0.053t) Now a property of math is Ln(ex) is always equal to x So Ln(e20) = 20 Take that to our formula and we get Ln(3) = 0.053t Divide both sides by 0.053 to get our t. You can jut plug this into a calculator... t = 20.728 or 21 years to triple your investment.
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