Find the amount accumulated future value in the sinking fund if $1,200 is deposited quarterly for 10 years at 6% per year.
To find the amount accumulated future value in the sinking fund, we can use the formula for compound interest. The formula is:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated future value
P = Principal amount (the amount deposited)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, the principal amount (P) is $1,200, the annual interest rate (r) is 6% (or 0.06), the number of times interest is compounded per year (n) is 4 (quarterly deposits), and the number of years (t) is 10.
Substituting the values into the formula:
A = 1200(1 + 0.06/4)^(4*10)
Simplifying:
A = 1200(1 + 0.015)^40
Calculating:
A ≈ 1200(1.015)^40
Using a calculator or spreadsheet, you can raise 1.015 to the power of 40 and then multiply it by 1200 to find the accumulated future value of the sinking fund. The result will be the amount accumulated after 10 years.