# Future Value Of Future Value

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A mathematical model for the Future Value of a savings account earning interest that is
compounded continuously is given by the equation FV = Pert, where FV is the amount after t years,
P is the principal amount invested at t = 0, and the principal is assumed to grow continuously at a
rate, r. How many years will it take the principal to triple if the annual rate is 12%?
Solution;
FV = Pert,
FV is the amount after t years,
P is the principal amount invested at t = 0,
principal is assumed to grow continuously at a rate, r = 12
P is the principal = 1
Fv = 3
3 = 1 x e(12/100) x t
Introduce the natural log
Ln 3 = (0.12) x t
Time = ln 3 / (0.12)
Time = 1.09861228 /0.12
= 9.15510

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A mathematical model for the Future Value of a savings account earning interest that is compounded continuously is given by the equation FV = Pert, where FV is the amount after t years, P is the principal amount invested at t = 0, and the principal is assumed to grow continuously at a rate, r. How m ...
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