Find the amount accumulated in the sinking fund if $200 is deposited monthly for 14 years at 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest dollar.)
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.)
monthly rate = .03/12 = .0025
no of months in 14 years = 168
so Amount = 200[1.0025^168 - 1]/.0025
= $41693 to the nearest dollar
To calculate 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 = Accumulated amount
P = Monthly deposit
r = Interest rate per compounding period
n = Number of compounding periods
Plugging in the given values:
P = $200 (monthly deposit)
r = 3% per year (divide by 100 to convert to decimal)
n = 14 years (since there are 12 months in a year, this gives us 14 * 12 = 168 compounding periods)
Now we can calculate the accumulated amount:
A = 200 * ((1 + 0.03)^168 - 1) / 0.03
Using a calculator or a spreadsheet program, we find that the accumulated amount is approximately $46,667.