Question

The relationship between the capital recovery factor and sinking fund factor in a uniform series of payments is given by
1. Capital recovery factor = Sinking fund factor - Interest rate
2. Capital recovery factor = Sinking fund factor - (Interest rate)²
3. Capital recovery factor = Sinking fund factor + (Interest rate)²
4. Capital recovery factor = Sinking fund factor + Interest rate

Answer 1

Correct Answer - Option 4 : Capital recovery factor = Sinking fund factor + Interest rate

Explanation:

For uniform payment series capital recovery factor (CRF) is given by

\(CRF = \frac{{i{{\left( {1 + i} \right)}^n}}}{{{{\left( {1 + i} \right)}^n} - 1}}\)        .....(1)

For uniform payment series sinking fund factor is given by

\(SFF = \frac{i}{{{{\left( {1 + i} \right)}^n} - 1}}\)        .....(2) 

where, i = interest rate

Add 'interest rate (i)' in equation (2)

\(SFF + i = \frac{i}{{{{\left( {1 + i} \right)}^n} - 1}} + i = \frac{{i + i{{\left( {1 + i} \right)}^n} - i}}{{{{\left( {1 + i} \right)}^n} - 1}} = \frac{{i{{\left( {1 + i} \right)}^n}}}{{{{\left( {1 + i} \right)}^n} - 1}}\)

So, SFF + i = CRF