Jill has 10,000 to invest at time t = 0 and two possible ways to invest it. i) Investment A has a force of interest begin mathsize 12px style delta subscript t space equals space fraction numerator 0.07 over denominator 1 plus 0.07 t end fraction end style at time t. ii) Investment B provides a 4.2% effective annual interest rate. Note: for effective interest rate i, the force of interest is ln(1+i) Jill can invest any portion of her principal in either investment A or B, and can transfer any portion of her money between the two investments at any time. What is the maximum amount Jill can accumulate by time t = 20? Hint: The maximum value does not require Jill to split her principal. Only transfer all of the funds from investment A to investment B at a specific time. Draw a graph of the two force of interest functions between t=0 and t=20 to determine on which interval each account earns the higher force of interest . You will need to determine the time at which the forces are equal to help you determine how long each investment should be made. Determine the accumulation functions for investment A and investment B.