The correct answer is: Uniform series sinking fund factor.
A sinking fund is a fund that is set aside to pay off a debt or liability. The uniform series sinking fund factor is used to calculate the amount of money that needs to be deposited into the sinking fund each period in order to have enough money to pay off the debt or liability at the end of the term.
The formula for the uniform series sinking fund factor is:
$$\frac{{{\text{i}}{{\left( {1 + {\text{i}}} \right)}^{\text{n}}}}}{{{{\left( {1 + {\text{i}}} \right)}^{\text{n}}} – 1}}}$$
where:
- i = the interest rate
- n = the number of periods
The uniform series sinking fund factor can be used to calculate the amount of money that needs to be deposited into a sinking fund each period to pay off a debt or
liability. For example, if you have a debt of $10,000 that you want to pay off in 5 years at an interest rate of 5%, you would need to deposit $2,089.44 each year into a sinking fund to have enough money to pay off the debt at the end of the term.The other options are incorrect because they do not describe the formula that is given in the question.
- Capital recovery factor: The capital recovery factor is used to calculate the amount of money that needs to be paid each period to recover the cost of an asset over its lifetime.
- Single payment present worth factor: The single payment present worth factor is used to calculate the present value of a single payment that will be received in the future.
- Uniform gradient future worth factor: The uniform gradient future worth factor is used to calculate the future value of a series of equal payments that are made at regular intervals over a period of time.