Find the amount accumulated in the sinking fund if $1600 is deposited quarterly for 20 years at 6% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest dollar.)
To find the amount accumulated in the sinking fund, we can use the formula for the future value of an ordinary annuity:
A = P * ((1 + r)^(n*t) - 1) / r
Where:
A = amount accumulated in the sinking fund
P = periodic deposit
r = interest rate per period
n = number of compounding periods per year
t = number of years
In this case, the periodic deposit (P) is $1600, the interest rate per period (r) is 6% or 0.06, the number of compounding periods per year (n) is 4 (since it's deposited quarterly), and the number of years (t) is 20.
Substituting these values into the formula:
A = 1600 * ((1 + 0.06)^(4*20) - 1) / 0.06
Calculating this expression gives us the amount accumulated in the sinking fund.
Note: The caret symbol (^) represents exponentiation.