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What is a Sinking Fund?
A Sinking Fund is a special fund that is created by depositing fixed payments each period to gain an estimated and fixed amount after a specific period. In other words, a sinking fund is an account that earns compound interest into which a fixed payment is made periodically for a specific period of time.
A sinking fund is generally created to accumulate a fixed sum of money after a specific period. One can use the sinking fund to pay off a loan as a lump sum after a certain period. In the meantime, until the lump-sum period is reached, one can just keep paying the loan interest.
Note − Sinking Funds are a great way to calculate the future payment of a fund. It is useful in many ways and is used extensively. Many types of loans usually prefer the sinking fund method, as it is both reliable and rewarding.
Example
Suppose a person borrows INR 5,000 and wants to pay back the amount in 2 years from now. He agrees to pay a monthly interest of 10% and sets up a sinking fund for the lump-sum payment.
The sinking fund earns 7% interest compounded yearly. The monthly payment includes both the interest payment and the payment for the sinking fund. So, how much should he pay each month?
The interest rate based on the fund is 10%, so let's use the simple interest formula,
I = P × r × t
I = 5000 (0.10) (1) = 500 per year
In monthly terms = 500 /12 = 42
This is the interest rate. Next, we have to consider the payment in the fund.
$$P=\frac{A\times i}{(1+i)^{n}-1}$$
where P is the amount of the payment, A is the amount to be accumulated, i is the interest rate per time period, and n is the number of time periods.
Here, A = 5000, i = 7, and n = 2
$$P=\frac{5000\times 7}{(1+7)^{2}-1}$$
$$P=\frac{3500}{64-1}=555.6$$
So, the net amount payable yearly is,
555.6 + 42 = $597.50
Note − Sinking Funds are a great tool for lenders to lend money to borrowers, as they get the interests in between and the lump-sum at the end of the tenure of the fund.
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