Bir Borcun Ritmik Atlamalı Sabit ve Geometrik Değişimli Taksitlerle Geri Ödenmesi Problemleri İçin Genel Formüller

Öz

Nowadays, the periodic level payment model is the most widely used loan payment model by the banks. In addition, the periodic geometric and linear gradient payment models are available in the financial mathematics books. The arbitrary skip periodic level (or equal) loan payment model was firstly developed by Formato (1992). Formato’s model was extended to the geometric gradient loan payment model by Moon (1994) and the linear gradient model by Eroglu and Karaoz (2002). This loan payment models that have periodic level and geometric gradient series payment with rhythmic skips instead of arbitrary skips have been discussed. General formulae have been derived for these models. Numerical examples are solved to show the practical application of the developed payment models on home financing.

Anahtar Kelimeler

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Bir Borcun Ritmik Atlamalı Sabit ve Geometrik Değişimli Taksitlerle Geri Ödenmesi Problemleri İçin Genel Formüller

Öz

Bankalar tarafından en çok kullanılan borç ödeme modeli, sabit taksitli modeldir. Bunun yanı sıra, finans matematiği kitaplarında geometrik ve aritmetik değişimli taksitlerle borç ödeme modelleri de mevcuttur. Rastgele atlamalı sabit taksitli borç ödeme modeli Formato (1992) tarafından geliştirildi. Formato’nun modeli; Moon (1994) tarafından geometrik değişimli taksitlerle ve Eroğlu ve Karaöz (2002) tarafından aritmetik değişimli taksitlerle borç ödeme modellerine genişletildi. Bu çalışmada, rastgele atlamalı sabit ve geometrik değişimli taksitler yerine, ritmik atlamalı sabit ve geometrik değişimli taksitler içeren borç ödeme modelleri ele alınıp modeller için genel formüller türetilmiştir. Geliştirilen ödeme modellerinin pratik uygulamasını göstermek için sayısal örnekler konut finansman modeli kurularak çözülmüştür.

Anahtar Kelimeler

• Anüite
• Ritmik atlamalı
• Rastgele atlamalı
• Borç ödeme modelleri

Kaynakça

1. BASKAYA, Z., (1998). “Business Mathematics”. 1. Edition, In Turkish, Ekin Publishing, Bursa, Turkey, 83.
2. EROGLU, A., (2000). ”Solution Approaches for Repayment Problems”. Suleyman Demirel University Journal of Economics and Administrative Science Faculty, 5, (1), 87-102.
3. EROGLU, A., (2001), “Solution Approaches for in a Skip Repayment Problems with Piecewise Geometric-Gradient and ArithmeticGradient Payment Series”. Dumlupinar University Journal of Social Sciences, 5, 297-307.
4. EROGLU, A., KARAOZ, M., (2002). “Generalized Formula for the Periodic Linear Gradient Series Payment in a Skip Payment Loan with Arbitrary Skips”. The Engineering Economist, 47 (1), 75-83.
5. EROGLU, A., KALAYCI S., OZDEMIR, G., CETIN, A.C., USUL, H., (2012). “Generalized Formulae for Islamic Home Financing through the Musharakah Mutanaqisah Contracts”. Afro Eurasian Studies, 1 (1), 126-133.
6. FORMATO, R.A., (1992). “Generalized Formula for Periodic Payment in a Skip Payment Loan with Arbitrary Skips”. The Engineering Economist, 37 (4), 355-359.
7. GALBIATI, M., SORAMÄKI, K., (2011). “An agent-based model of payment systems”. Journal of Economic Dynamics & Control, 35, 859-8
8. ISCIL, N., (1997). “Business Arithmetics and Financial Algebra”. Armagan Publishing, Ankara, Turkey, pp. 148. KIM, Y. S., LEE, M., (2010). “A model of debit card as a means of payments”. Journal of Economic Dynamics & Control, 34, 135913

9. MARTIN, A., ORLANDO, M. J., SKEIE, D., (2008). “Payment networks in a search model of money”. Review of Economic Dynamics, 11, 104-132.
10. MILLS, JR. D. C., (2006). “Alternative central bank credit policies for liquidity provision in a model of payments”. Journal of Monetary Economics, 53, 1593-1611.
11. MOON, I., (1994). “Generalized Formula for the Periodic Geometric-Gradient Series Payment in a Skip Payment Loan with Arbitrary Skips”. The Engineering Economist, 39 (2), 177-185.