MATH SOLVE

3 months ago

Q:
# An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation mc022-1.jpg represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.

Accepted Solution

A:

Answer:7 yearsStep-by-step explanation:An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously.Formula:[tex]A=Pe^{rt}[/tex]Where, A is amount, A=350P is principle, P=200R is rate of interest, r=0.08t is time, t=?Substitute the value into formula [tex]350=200e^{0.08\cdot t}[/tex][tex]e^{0.8t}=1.75[/tex]Taking ln both sides [tex]0.08t = ln(1.75)[/tex][tex]t=6.99\approx 7[/tex]Hence, 7 years ago money was invested.