a. To determine which investment would be worth more after 20 years, we can use the formula for continuous compounding and quarterly compounding respectively:
Investment A: A = Pe^(rt), where P = $800, r = 0.035, and t = 20
A = 800e^(0.035*20) = $1,641.95
Investment B: A = P(1 + r/n)^(nt), where P = $900, r = 0.03, n = 4 (since it's compounded quarterly), and t = 20
A = 900(1 + 0.03/4)^(4*20) = $1,617.45
Therefore, Investment A would be worth more after 20 years.
b. To find out how long it will take Investment A to triple, we can use the formula for continuous compounding:
A = Pe^(rt), where P = $800, A = 3P = $2,400, and r = 0.035
2.4 = 800e^(0.035t)
e^(0.035t) = 3
0.035t = ln(3)
t = ln(3)/0.035
t ≈ 19.9 years
Therefore, it will take Investment A approximately 19.9 years to triple. Rounded to the nearest tenth of a year, it will take 19.9 years.