3. Assume a force of interest of 8(t) = 0.10+ 0.24t² a. Calculate the values of the nominal rates of interest i(2), (12) and (365) at the start of the year that would produce the same accumulated values at time t = 1, t= and t = 35 as would have been produced if the force of interest 8(t) had acted on the fund for those respective time periods. b. Calculate the values of the nominal rates of interest (²), (12) and (365) at the start of the second year that would produce the same accumulated values at time t = 1+1, t=1+1 and 1=1+35 as would have been produced if the force of interest 8(t) had acted on the fund for those respective time periods. c. What do you think the limit as n→∞oof (*) would be in those two situations?

B A 10 5x+10 D, 14 E

I

A 13 5 B 12

Let AABC be a triangle. Fix the points X, Y, and Z on AB, AC, and BC, respectively (as in the figure) such that BX = - = CZ AY = 4. Assume that the area of AXYZ is one and calculate the area of AABC. ХА YC ZB

19 a-c