ОПТИМИЗАЦИЯ СХЕМ ИПОТЕЧНОГО КРЕДИТОВАНИЯ1

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<ul><li><p> . . . . </p><p>2013 15 (158). 27/1 </p><p> 303.732.4 </p><p> 1 </p><p> . , , . </p><p> . , , , . , , , . </p><p> : , , , . </p><p> . , , : </p><p>1) ; 2) ; 3) ; 4) . </p><p> . . </p><p> 19 2010 . 1201- 2030 , . , , 60 . , () - , . (), . , , : </p><p>1) ; 2) </p><p>; 3) </p><p> : - ; 4) ( ) </p><p> . </p><p> 2012- : </p><p>88 </p><p>.. . </p><p>e-mail: 376310@bsu.edu.ru </p><p> 11-07-00154 </p><p>mailto:376310@bsu.edu.ru</p></li><li><p>89 . . . . 2013 15 (158). 27/1 </p><p> (. .) </p><p> 2012 2011 (%) </p><p> 445 665 320 712 38,96 </p><p>24 157 608 80 382 96,07 </p><p> 64 201 45 690 40,51 </p><p> 22 635 18 144 24,75 </p><p> 17 637 13 084 34,79 </p><p> 1, , , , , . , 2030 : 60% , , 2010 . </p><p> , : </p><p>1) , , ; 2) , </p><p> ; </p><p>3) , ; </p><p>4) , . </p><p>, 2030 , - , . , (, , ), - . </p><p>- . , : (x,t), - , t - , - . : t , x. - , . ( ) , , ( ) - , . </p><p> (, , ) , </p><p>1 : http://www.gks.ru/bgd/regl/b12_13/IssWWW.exe/Stg/d1/06-49.htm ( : 20.03.2013). </p><p>http://www.gks.ru/bgd/regl/b12_13/IssWWW.exe/Stg/d1/06-49.htm</p></li><li><p>90 . . . . 2013 15 (158). 27/1 </p><p> . . 1 , 1. 3 . . 70% (30% ), 3 12% . </p><p>j 1 I FinStream - </p><p>j i j i j d i j t ^ c a , </p><p> : 24 .03 .2013. : 24.03.2016. ( ): 1096 </p><p>: 12 .655831% j :. 1:1:" NPV= 74657.09 &amp;. </p><p>3 </p><p>2 </p><p>1 </p><p>X </p><p>-1 </p><p>_2 </p><p>-3 = 1000000 . </p><p>&lt; 2 0 1 3 </p><p> 6 </p><p>1 5 2 6 2 7 2 8 1 2 3 </p><p>4 5 6 7 8 9 1 0 </p><p>1 1 1 2 1 3 1 4 1 5 1 6 1 7 </p><p>1 8 1 3 2 0 2 1 22 2 3 \ </p><p>2 5 2 6 2 7 2 8 2 9 3 0 3 1 </p><p>1 2 3 4 5 6 7 </p><p>I I : 2 4 3 2 0 1 3 </p><p>( * ) </p><p> (.) </p><p> 24.03.2012: -21 DDDDD.DD . 2 4 . 0 4 . 2 0 1 3 : 6 9 7 5 0 . 0 5 . </p><p> 2 4 . 0 5 . 2 0 1 3 : 6 9 7 5 0 . 0 5 . 2 4 . 0 6 . 2 0 1 3 : 6 9 7 5 0 . 0 5 . 2 4 . 0 7 . 2 0 1 3 : 6 9 7 5 0 . 0 5 . 2 4 . 0 S . 2 0 1 3 : 6 9 7 5 0 . 0 5 . 24 09 2 0 1 3 : 6 9 7 5 0 . 0 5 </p><p> 2 4 . 1 0 . 2 0 1 3 : 6 9 7 5 0 . 0 5 . </p><p>F &lt; 3 1 I </p><p>. 1. </p><p> . 1 FinStream [1], , . </p><p> , 24.03.2013 2.1 . . ( ), 3- ( ). 70 . ., , . </p><p> , , , , . </p><p> / ) } = 1 , </p><p>, , NPV (Net Present Value). r, , </p><p>1 - FinStream: .. FinStream// , - 2011615994 3 2011. </p></li><li><p>91 . . . . 2013 15 (158). 27/1 </p><p> . , , . </p><p> t0 {(^ ,t/ )} , NPV, </p><p> t0, : </p><p> ' - , t0 - . , , </p><p>, , </p><p> V = (1 + r )-1 , 0 1. (1) NPV : </p><p>NPV ( ,ti ) L t,V ) = f - . (2) i = 1 </p><p> NPV : CF (Cash Flow), t0 </p><p> r = V 1 1, , . N - , , () . </p><p> NPV , , NPV=0 , . , NPV . , (3), IRR (Internal Rate of Return): </p><p> , ^ f ^ + = 0 - (3) , NPV, , , </p><p> , (3) . . , . </p><p> : , . , , . , , . , , () , . </p><p> , , , ( ) . , , , . , </p></li><li><p>,|2g Ijffl . . . . I 2013 15 (158). 27/1 </p><p> , . </p><p> : , , 10- . : , , , , . </p><p> , , : </p><p>1) ; 2) ; 3) ; 4) . </p><p> [2-4]. , , 70% , . : </p><p>- ; </p><p>- (), ( ) . </p><p> , , , , , . , , ( ) , , . , . </p><p> , , . -, , 1 , , 1 , 1/12 . Vm, , Vy, : </p><p>Vy = Vm . m (month) y (year) , , . ( ) ( ), . (, FinStream) , . </p><p>-, j r, : rm ry, . , , .. . , </p></li><li><p>93 . . . . 2013 15 (158). 27/1 </p><p> (3), ( , ..) , , . ( ) , , . </p><p>-, n (ni 2 ) , 12; .. . </p><p> , A, - B. , A=B. , , . </p><p>, &gt; B, ( ) . </p><p> , , . 2 ( N - ). </p><p>A A A B B B </p><p> k . . n 1 1 </p><p>1 " " 1 </p><p>0 1 .... 1-1 n1+1 n1+2 .... n1+n2 </p><p>N </p><p>. 2. </p><p> . 2 : ( ) ni ( ) ( ) n2 ( ). ni N. </p><p> . ( , ..) . , . </p><p> , ( ) , , . : , , .. (3). </p></li><li><p>,|2g Ijffl . . . . I 2013 15 (158). 27/1 </p><p> , , , - . </p><p> : , . 2 , (3) . </p><p> , . </p><p> Z : Z A n 1 + B n 2 . NPV V [5]: </p><p>\NPV (V) 0, </p><p>\NPV'(V) 0, ( 4 ) </p><p> , r V - 1 -1 () , . </p><p> . 2, NPV(V): </p><p>NPV (V) A + AV +... + AVn 1 -1 - NVn1 + BVn1 +1 + . . . + BVn1+n2 </p><p> A(1 + V + . . . + Vn1 - 1 ) - N V n 1 + BV n 1 +1 (1 + V + . . . + V n 2 - 1 ) </p><p>1 - V n 1 ,1 - Vn ' I T T T ^ T i T r n + 1 - 1 (5) </p><p>A NVn1 + BV"^ 1 - V 1 - V </p><p> (5), , N P V ( V ) ( V ) / ( 1 - V ) , P(V) : </p><p>P(V) a ( 1 - Vn1)- NVn1 (1 - V)+ BVn1 + 1 (1 - Vn2). (6) </p><p> , 2, 2. , (17) : </p><p>P(V) 0 </p><p>P'(V) 0 , ( 7 ) , B, n1, n2. A, B, n1, n2, V, N . V N , : V , N , . </p><p> A, B, ni, n2 . , (26). A B ( ), n1 n2 , , A B . </p></li><li><p>95 . . . . 2013 15 (158). 27/1 </p><p> (26) P(V), A B : </p><p>A(1 - V n 1 ) + B ( ( " 1 + 1 - V n 1 + n 2 + 1 ) N ( V n - V n 1 + 1 ) </p><p>\ A(-n1Vn1 - 1 ) + B((n1 + 1)Vn1 - (n1 + n2 + 1)Vn1 + n 2 ) N(n1Vn1 - 1 - (n1 + 1)Vn1) ( 8 ) </p><p> (8) , A B . . , Z Z A n 1 + Bn 2, w : </p><p>. , 1 3 2 2 2 3 1 2 - I 1 1 2 3 2 1 1 3 </p><p>W 7 7</p><p> n 1 + n 2 , (9) </p><p>N 1122 - 1 2 2 1 a 1 1 a 2 2 - 1 2 2 1 </p><p>a 1 - V"1 a^ Vn1 - Vn1 + n 2 + 1 a^ Vn1 - Vn1 + 1 a^ - n Vn1 - 1 11 , 1 2 , 1 3 , 2 1 1 2 2 (n1 + 1)Vn1 - (n1 + n2 + 1)Vn1 + n 2 , 2 3 n V n 1 - 1 - ( + 1)Vn1 . </p><p> w ( V=i/(i+r)), n n1 (n2=n-n1). : </p><p>1) n ( ); </p><p>2) n1 ( ); </p><p>3) (29) A, B (30) w, ; </p><p>4) n1 3 n1 = 0; </p><p>5) n1, w . , </p><p>n1 . A, B w. , , . , , 4. </p><p> , , (, , , ). , . </p><p> 3 3000000 ., 15 . 12% , - 5 (, 10=15-5 ). . 3 , 22091,39 ., - 16909,94 . </p></li><li><p> . . . . </p><p>2013 15 (158). 27/1 </p><p> 3000000 . 3354675,95 . , w 1,118225318. </p><p> , 12% , . , . </p><p> (4) , . , , . w , . . ( ) . </p><p> . </p><p> : . , . , , . . </p><p>96 </p><p>^ 1 </p><p>j j d ^ i ^ g i ^ a i A ^ a - y i ^ - a, s - al si 1 </p><p>^ 100% ~ </p><p>&amp; </p><p>Arial ~ 10 13 </p><p>- s | | % A i l fx </p><p> F G 1 2 N= 3 0 0 0 0 0 0 &amp;. 3 15 180 4 1= 5 60 2= 10 120 6 = 12 % () 0 . 9 4 8 8 7 9 2 9 3 %[ ) 7 V= 0 , 8 9 2 8 5 7 1 4 3 0 . 9 9 0 5 0 0 3 9 8 8 11 = 0 . 4 3 2 5 7 3 1 4 4 1 2 = 0 . 3 8 1 1 1 4 2 8 1 3 = 0.00&amp;333&amp;87 9 21 = -34.3831 2 2 = 1 , 5 4 5 0 1 4 9 1 2 3 = - 0 . 2 4 4 3 7 5 0 9 9 10 = 2 2 0 9 1 . 3 9 . 11 1 5 9 0 9 . 9 4 . 12 w= 1 . 1 1 8 2 2 5 3 1 8 13 Z= 3 3 5 4 6 7 5 , 9 5 &amp;. 14 15 15 17 18 </p><p>N \ 1 / 2 / / 1 ' I I </p><p>. 3. </p><p> . , . </p></li><li><p>97 . . . . 2013 15 (158). 27/1 </p><p> . , , , . </p><p> , , . , , . , , . </p><p> , . , , , ( , ). , . </p><p> , . </p><p> 1. , .. - -</p><p> / .. , .. , .. // -. (). 2012. 1. .130-139. </p><p>2. , .. / .. -, .. , .. // -. . . . . 2010. 19 (90). 16/1. .120-127. </p><p>3. , .. - / .. , .. , .. // . . . . . 2011. 7 (102). 18/1. .102-109. </p><p>4. , .. / .. , .. , .. // - . . . . . 2011. 13 (108). 19/1. .132-108. </p><p>5. , .. / .. , .. , .. // , 62. 1. 2012. . 91-100. </p><p>OPTIMIZATION OF A MORTGAGE LOAN </p><p>O.M.TUBOLTSEVA Belgorod State National Research University Belgorod </p><p>e-mail: 376310@bsu.edu.ru </p><p>The problems of optimization schemes of mortgage lending. The standard scheme of mortgage lending, having a number of advantages over alternative methods of housing loans, require significant costs for servicing the loan. </p><p>The need to consider non-standard mortgage schemes determined the ur-gent need to improve the availability of mortgages to the general public. In par-ticular, the practice needs require consideration of new combination regimens mortgage when first performed, followed by the accumulation of funds lending. Since the classical method based on the use of annuities do not provide optimal solutions, new approaches are applied to the optimization of mortgage schemes. </p><p>Keywords: optimization, a mortgage, a combined scheme, systematic ap-proach. </p><p>mailto:376310@bsu.edu.ru</p></li></ul>