Answer:
a A=$47,887.81
b.A=$46,430.80
Step-by-step 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;
[tex]i_m=(1+i/m)^m-1\\\\=(1+0.06/365)^{365}-1\\\\=0.06183[/tex]
#We use the calculated effective rate, 0.06183, to solve for the future value as:
[tex]A=P(1+i_m)^n\\\\=40000(1.06183)^3\\\\=47887.81[/tex]
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:
[tex]i_m=(1+i/m)^m-1\\\\=(1+0.05/4)^4-1\\\\=0.05095[/tex]
#We use the calculated effective rate, 0.05095, to solve for the future value as:
[tex]A=P(1+i_m)^n\\\\=40000(1.05095)^3\\\\=46430.80[/tex]
Hence, the future value of the sinking fund is $46,430.80
