Final answer:
To find the future value of the sinking fund, the future value of an annuity formula is used with quarterly deposits of $4 million, an annual interest rate of 5.8% compounded quarterly over 20 years, resulting in approximately $209.35 million in the fund.
Step-by-step explanation:
The question asks how much money will be in a sinking fund after 20 years if $4 million is deposited at the end of each quarter at an annual interest rate of 5.8% compounded quarterly. To solve this, we need to use the formula for the future value of an annuity compounded quarterly:
FV = P × { [ (1 + r/n)^(nt) - 1 ] / (r/n) }
Where FV is the future value, P is the periodic payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years. Using this, we plug in the values:
P = 4 million dollars
r = 5.8%
n = 4 (quarterly)
t = 20 years
Calculating these we get:
FV = 4 × { [ (1 + 0.058/4)^(4×20) - 1 ] / (0.058/4) }
After calculating, the future value (rounded to two decimal places) gives us $209.35 million in the sinking fund after 20 years.