A person invests $1,450 in an account that earns 6% annual interest compounded continuously. Find when the value of the investment reaches $2,500. If necessary round to the nearest tenth. The Investment will reach a value of $2.500 in approximately ____ years.
Accepted Solution
A:
Answer:20.7 yearsStep-by-step explanation:Use the "compound amount, compounding continuously" formula:A = Pe^(r · t) Here, A = $2,500 = $1,450e^(0.06 · t)Divide both sides by $1,450: 1.724 = e^(0.06 · t)Taking the natural log of both sides, we obtain:ln 1.724 = (0.06 · t).Finally, we divide both sides by 0.06, obtaining:ln 1.724------------ = t = 20.7 0.06The Investment will reach a value of $2.500 in approximately 20.7 years.