Development of periodic loan repayment models considering rhythmic skips

The notion of loan repayments rest on the principle that present value of sum of the instalments are equal to present value of the loan total. In a standard loan repayment plan, periodic instalments are set to a fixed amount. Besides, loan repayment plans with geometrically or arithmetically increasing periodic amounts can also be found at mathematics of finance textbooks. Beyond that models for loan repayments with skips deal with types of loans in that some periods are predetermined to pass by without making any instalment. Payment skips in some periods have been requested by some clients as expenses in some months rise considerably. In this study, general formulas are derived under the assumptions that periodic loan repayments adjust with arithmetic gradient series and interrupt with rhythmic non-payment periods. Later, by setting the arithmetic change to zero, a general formula for loan repayment with equal periodic instalments that also has rhythmic skips has been derived. Same numerical examples with solutions are presented for the developed models. As a result numerical examples have been used in order to show the validity of the models.