. A sinking fund is the accumulated amount to be realized at some future date (the end of the term) when a fixed number of periodic payments are paid into an account earning interest at the rate of i per period
Some kind of math ...
Even then, what is the question here?
http://www.financial-dictionary.thefreedictionary.com/Sinking fund
To calculate the accumulated amount in a sinking fund, you need to consider the following variables:
1. Periodic Payment: This is the amount of money deposited into the sinking fund account at regular intervals. Let's denote it as P.
2. Interest Rate: The rate of interest that the sinking fund account earns per period is denoted as i. It is usually expressed as a decimal value.
3. Number of Periods: The length of time over which the periodic payments are made into the sinking fund account is denoted as n.
To calculate the accumulated amount in the sinking fund, you can use the formula for the future value of an ordinary annuity:
A = P * ((1 + i)^n - 1) / i
Or, alternatively, you can break down the calculation into several steps:
1. Calculate the compound interest factor:
FVIF = (1 + i)^n
2. Subtract 1 from the compound interest factor:
FVIF_minus_1 = FVIF - 1
3. Divide the periodic payment by the interest rate:
Payment_by_rate = P / i
4. Multiply the payment by rate with the compound interest factor minus 1:
Amount = Payment_by_rate * FVIF_minus_1
Hence, the accumulated amount in the sinking fund would be equal to Amount.
Keep in mind that this formula assumes that each period's payment is made at the end of the period and that the compounding periods align with the payment periods.