A Model Based on Average Investment for Solving Complex Annuity Problems of Sinking Fund

Undoubtedly, the basic sinking fund formula gives the future value of a series of equal installments. The main underlying assumption for using this formula is that installment and compounding frequency must be in equal interval. But when installment for a deposit scheme or any other savings scheme and compounding frequency do not occur in an equal interval, which is treated as the complex annuity problems in Finance Literature, the basic sinking fund formula does not give the accurate result. As a result, the obtainable amount from different deposit schemes offered by different banks and financial institutions does not match with the amount of future value calculated through the basic sinking fund formula by the investors or savers. This study focuses the concealed facts for such type of mismatches in values and at the same time it provides a solution through developing a new formula by extending the basic formula intended not only to remove those mismatches but also get the accurate future value from a sinking fund provision in case of complex annuity. Besides, since banks and financial institutions calculate the interest on the average amount of equal installments deposited within a period of time due to complex annuity, the study also formulates an arithmetic formula for calculating the average amount of installment.