Answer:
a A=$47,887.81
b.A=$46,430.80
Explanation:
a. Given the initial amount is $40,000 with a 3-year term and a 6% rate compounded daily.
-Take 1 year=365 days
#First we calculate the effective interest rate corresponding to the daily compounding;

#We use the calculated effective rate, 0.06183, to solve for the future value as:

Hence, the total future value for a daily compounding is $47,887.81
b. For a sinking fund with a 5% compounded quarterly:
#We calculate the annual effective rate:

#We use the calculated effective rate, 0.05095, to solve for the future value as:

Hence, the future value of the sinking fund is $46,430.80