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Identify the correct relationship for annual sinking fund. Where, I = Annual sinking fund, S = Total amount of sinking fund invested on that i = Rate of interest n = number of years required to get тАШSтАЩ
The annual sinking fund is the fixed annual amount that must be deposited into a fund at a specific interest rate so that the total accumulated amount equals a target sum (S) at the end of a specified period (n). The mathematical relationship is derived from the future value of an ordinary annuity formula, where the annual payment I is I=(1+i)nтИТ1SтЛЕiтАЛ.
The annual sinking fund is the fixed annual amount that must be deposited into a fund at a specific interest rate so that the total accumulated amount equals a target sum (S) at the end of a specified period (n). The mathematical relationship is derived from the future value of an ordinary annuity formula, where the annual payment I is I=(1+i)nтИТ1SтЛЕiтАЛ.
I=(1+i)nтИТ1SтЛЕiтАЛ тАФ Formula for annual sinking fund, where I is the annual payment, S is the total sum required, i is the interest rate, and n is the number of years.
The sinking fund method assumes that the capital required for the replacement of an asset at the end of its useful life is accumulated by setting aside equal annual payments. These payments are invested at a compound interest rate, causing the fund to grow through both the annual deposits and the earned interest until it reaches the required total capital.
The sinking fund method is commonly used for the depreciation of assets in valuation and estimation.
The rate of interest (i) is expressed as a decimal (e.g., 5% = 0.05).
This method is preferred for infrastructure assets where a large sum is needed for replacement at the end of the service life.
Ensures funds are available exactly when the asset reaches the end of its useful life.
Provides a systematic way to account for heavy capital replacements.
It is sensitive to market interest rate fluctuations.
Assumes the rate of interest remains constant throughout the period.
Depreciation of machinery and buildings.
Accumulating funds for debt redemption.
Option D is the only mathematically correct derivation of the sinking fund factor based on the future value of an ordinary annuity.
The other options erroneously swap variables like n and i or rearrange the power index, which does not represent the correct compounding interest formula.
D is correct тАФ The annual sinking fund I is calculated using the formula I=(1+i)nтИТ1SтЛЕiтАЛ.
Always remember that in the denominator (1+i)nтИТ1, i is the interest rate and n is the duration in years; mixing them up is a common error in civil engineering exams.
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