A sum of money, A₀, is invested at a certain fixed interest rate, and this interest is compounded continuously. After 7 years, the money has doubled. The balance at the end of 14 years is $4 A _ { 0 }$ .

Question

Quizplus · Accepted Answer

When interest is compounded continuously, the formula for the future value of an investment is $A = P e^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. If the money doubles in 7 years, it means that $A = 2P$ when $t = 7$. Since the interest is compounded continuously, the investment will double again in another 7 years (making $t = 14$), resulting in $A = 4P$, where $P$ is the initial investment ($A_0$).

A Sum of Money, A0, Is Invested at a Certain 4A04 A _ { 0 }4A0​

A Sum of Money, A₀, Is Invested at a Certain $4 A _ { 0 }$