Find the amount accumulated in the sinking fund if $350 is deposited monthly for 14 years at 7% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest dollar.)
monthly rate = i = .07/12 = .0058333
number of payments = n = 14x12 = 168
Amount = 350[(1 + .0058333)^168 - 1]/.0058333
= 99412.84
or $99413 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 - 1) / r
Where:
A = amount accumulated in the sinking fund
P = monthly deposit
r = interest rate per compounding period
n = number of compounding periods
In this case, the monthly deposit (P) is $350, the interest rate (r) is 7% per year, and the deposit is made for 14 years. We need to convert the interest rate and the time to match the compounding period, which is monthly in this case.
First, let's calculate the interest rate per month:
monthly interest rate = (1 + annual interest rate)^(1/12) - 1
= (1 + 7%)^(1/12) - 1
= (1.07)^(1/12) - 1
≈ 0.005657
Next, let's calculate the number of compounding periods:
number of compounding periods = number of years * number of compounding periods per year
= 14 * 12
= 168
Now, let's plug in the values into the formula:
A = $350 * ((1 + 0.005657)^168 - 1) / 0.005657
Calculating this expression will give us the amount accumulated in the sinking fund. Rounding the answer to the nearest dollar will give the final result.