find the periodic payments necessary to accumulate the amount given in a sinking fund. Assume end of period deposits and compounding at the same intervals as deposits.

$70,000 in a fund
7% per year,
monthly payments for 5 years
Thank you your time is appreciated !

To calculate the periodic payments necessary to accumulate a specific amount in a sinking fund, you can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where:
FV is the future value of the sinking fund (in this case, $70,000)
P is the periodic payment (unknown)
r is the interest rate per period (in this case, 7% per year, which needs to be divided by the number of compounding periods per year)
n is the number of compounding periods (in this case, monthly payments for 5 years, so 5 * 12 = 60)

Let's calculate the periodic payments:

1. Convert the annual interest rate to a monthly interest rate:
Monthly interest rate = 7% / 12 = 0.5833% (0.07 divided by 12)

2. Substitute the values into the formula:
$70,000 = P * [(1 + 0.005833)^60 - 1] / 0.005833

Now, we need to solve this equation to find the value of P, the periodic payment. We can use trial and error or an online financial calculator to find the payment amount quickly.

Using an online financial calculator or spreadsheet, you can input the values and find that the monthly payment required to accumulate $70,000 in 5 years at a 7% annual interest rate is approximately $1,090.34.

Therefore, the periodic monthly payments needed for this sinking fund are approximately $1,090.34.