Question on Future value

User Generated

OyhrBprna

Mathematics

Description

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%?

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Explanation & Answer

Alright, since we are not given a particular starting amount, we will have to make some tricks to reach the goal.Since we want the final amount to be three times the principal, this means that we can rearrange the formula in this way:FV=3PSo that we get: 3P=P*e^(rt) ---->-----> 3=e^(rt) -----> Substituting the annual interest rate: 3=e^(0,12*t)--...


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