Question

In: Accounting

An amortized loan requires 500 end of month payments of 1, 2, 3, 4, ..., 499,...

An amortized loan requires 500 end of month payments of 1, 2, 3, 4, ..., 499, 500. The nominal interest rate is 6% convertible monthly. Find the outstanding balance of the loan immediately after the 5th payment.

(a) 30514.11 (b) 29342.46 (c) 29327.36 (d) 28619.77 (e) 31589.03

Solutions

Expert Solution

Answer:

Option (d) 28619.77 is correct

Interest Rate is taken as 0.50% (6%/12 months)

table given below

              
YEARS   CASH   DISC. @0.50%   PRESENT VALUE  
   FLOW          
0      1      
1   $1.00    0.995024876   $1.00   
2   $2.00    0.990074503   $1.98   
3   $3.00    0.985148759   $2.96   
4   $4.00    0.980247522   $3.92   
5   $5.00    0.975370668   $4.88   
6   $6.00    0.970518078   $5.82   
7   $7.00    0.96568963   $6.76   
8   $8.00    0.960885204   $7.69   
9   $9.00    0.95610468   $8.60   
10   $10.00    0.951347941   $9.51   
11   $11.00    0.946614866   $10.41   
12   $12.00    0.94190534   $11.30   
13   $13.00    0.937219243   $12.18   
14   $14.00    0.932556461   $13.06   
15   $15.00    0.927916877   $13.92   
16   $16.00    0.923300375   $14.77   
17   $17.00    0.918706841   $15.62   
18   $18.00    0.91413616   $16.45   
19   $19.00    0.909588219   $17.28   
20   $20.00    0.905062904   $18.10   
21   $21.00    0.900560104   $18.91   
22   $22.00    0.896079705   $19.71   
23   $23.00    0.891621597   $20.51   
24   $24.00    0.887185669   $21.29   
25   $25.00    0.88277181   $22.07   
26   $26.00    0.87837991   $22.84   
27   $27.00    0.874009861   $23.60   
28   $28.00    0.869661553   $24.35   
29   $29.00    0.865334879   $25.09   
30   $30.00    0.86102973   $25.83   
31   $31.00    0.856746   $26.56   
32   $32.00    0.852483582   $27.28   
33   $33.00    0.84824237   $27.99   
34   $34.00    0.844022259   $28.70   
35   $35.00    0.839823143   $29.39   
36   $36.00    0.835644919   $30.08   
37   $37.00    0.831487481   $30.77   
38   $38.00    0.827350728   $31.44   
39   $39.00    0.823234555   $32.11   
40   $40.00    0.819138861   $32.77   
41   $41.00    0.815063543   $33.42   
42   $42.00    0.8110085   $34.06   
43   $43.00    0.806973632   $34.70   
44   $44.00    0.802958838   $35.33   
45   $45.00    0.798964018   $35.95   
46   $46.00    0.794989073   $36.57   
47   $47.00    0.791033903   $37.18   
48   $48.00    0.787098411   $37.78   
49   $49.00    0.783182499   $38.38   
50   $50.00    0.779286068   $38.96   
51   $51.00    0.775409023   $39.55   
52   $52.00    0.771551267   $40.12   
53   $53.00    0.767712703   $40.69   
54   $54.00    0.763893237   $41.25   
55   $55.00    0.760092773   $41.81   
56   $56.00    0.756311217   $42.35   
57   $57.00    0.752548475   $42.90   
58   $58.00    0.748804453   $43.43   
59   $59.00    0.745079057   $43.96   
60   $60.00    0.741372196   $44.48   
61   $61.00    0.737683777   $45.00   
62   $62.00    0.734013709   $45.51   
63   $63.00    0.730361899   $46.01   
64   $64.00    0.726728258   $46.51   
65   $65.00    0.723112695   $47.00   
66   $66.00    0.719515119   $47.49   
67   $67.00    0.715935442   $47.97   
68   $68.00    0.712373574   $48.44   
69   $69.00    0.708829427   $48.91   
70   $70.00    0.705302912   $49.37   
71   $71.00    0.701793942   $49.83   
72   $72.00    0.69830243   $50.28   
73   $73.00    0.694828289   $50.72   
74   $74.00    0.691371432   $51.16   
75   $75.00    0.687931773   $51.59   
76   $76.00    0.684509227   $52.02   
77   $77.00    0.681103708   $52.44   
78   $78.00    0.677715133   $52.86   
79   $79.00    0.674343415   $53.27   
80   $80.00    0.670988473   $53.68   
81   $81.00    0.667650222   $54.08   
82   $82.00    0.664328579   $54.47   
83   $83.00    0.661023462   $54.86   
84   $84.00    0.657734788   $55.25   
85   $85.00    0.654462475   $55.63   
86   $86.00    0.651206443   $56.00   
87   $87.00    0.64796661   $56.37   
88   $88.00    0.644742896   $56.74   
89   $89.00    0.64153522   $57.10   
90   $90.00    0.638343502   $57.45   
91   $91.00    0.635167664   $57.80   
92   $92.00    0.632007626   $58.14   
93   $93.00    0.628863309   $58.48   
94   $94.00    0.625734636   $58.82   
95   $95.00    0.622621528   $59.15   
96   $96.00    0.619523909   $59.47   
97   $97.00    0.6164417   $59.79   
98   $98.00    0.613374826   $60.11   
99   $99.00    0.61032321   $60.42   
100   $100.00    0.607286776   $60.73   
101   $101.00    0.604265449   $61.03   
102   $102.00    0.601259153   $61.33   
103   $103.00    0.598267814   $61.62   
104   $104.00    0.595291357   $61.91   
105   $105.00    0.592329709   $62.19   
106   $106.00    0.589382795   $62.47   
107   $107.00    0.586450542   $62.75   
108   $108.00    0.583532878   $63.02   
109   $109.00    0.580629729   $63.29   
110   $110.00    0.577741024   $63.55   
111   $111.00    0.57486669   $63.81   
112   $112.00    0.572006657   $64.06   
113   $113.00    0.569160853   $64.32   
114   $114.00    0.566329207   $64.56   
115   $115.00    0.563511649   $64.80   
116   $116.00    0.560708108   $65.04   
117   $117.00    0.557918516   $65.28   
118   $118.00    0.555142802   $65.51   
119   $119.00    0.552380897   $65.73   
120   $120.00    0.549632733   $65.96   
121   $121.00    0.546898242   $66.17   
122   $122.00    0.544177355   $66.39   
123   $123.00    0.541470005   $66.60   
124   $124.00    0.538776125   $66.81   
125   $125.00    0.536095646   $67.01   
126   $126.00    0.533428504   $67.21   
127   $127.00    0.530774631   $67.41   
128   $128.00    0.528133961   $67.60   
129   $129.00    0.525506429   $67.79   
130   $130.00    0.522891969   $67.98   
131   $131.00    0.520290516   $68.16   
132   $132.00    0.517702006   $68.34   
133   $133.00    0.515126375   $68.51   
134   $134.00    0.512563557   $68.68   
135   $135.00    0.510013489   $68.85   
136   $136.00    0.507476109   $69.02   
137   $137.00    0.504951352   $69.18   
138   $138.00    0.502439156   $69.34   
139   $139.00    0.499939459   $69.49   
140   $140.00    0.497452198   $69.64   
141   $141.00    0.494977311   $69.79   
142   $142.00    0.492514738   $69.94   
143   $143.00    0.490064416   $70.08   
144   $144.00    0.487626284   $70.22   
145   $145.00    0.485200283   $70.35   
146   $146.00    0.482786351   $70.49   
147   $147.00    0.480384429   $70.62   
148   $148.00    0.477994457   $70.74   
149   $149.00    0.475616375   $70.87   
150   $150.00    0.473250124   $70.99   
151   $151.00    0.470895646   $71.11   
152   $152.00    0.468552881   $71.22   
153   $153.00    0.466221773   $71.33   
154   $154.00    0.463902261   $71.44   
155   $155.00    0.46159429   $71.55   
156   $156.00    0.459297801   $71.65   
157   $157.00    0.457012737   $71.75   
158   $158.00    0.454739042   $71.85   
159   $159.00    0.452476659   $71.94   
160   $160.00    0.450225531   $72.04   
161   $161.00    0.447985603   $72.13   
162   $162.00    0.445756819   $72.21   
163   $163.00    0.443539123   $72.30   
164   $164.00    0.441332461   $72.38   
165   $165.00    0.439136777   $72.46   
166   $166.00    0.436952017   $72.53   
167   $167.00    0.434778126   $72.61   
168   $168.00    0.432615051   $72.68   
169   $169.00    0.430462737   $72.75   
170   $170.00    0.428321132   $72.81   
171   $171.00    0.426190181   $72.88   
172   $172.00    0.424069832   $72.94   
173   $173.00    0.421960032   $73.00   
174   $174.00    0.419860728   $73.06   
175   $175.00    0.417771869   $73.11   
176   $176.00    0.415693402   $73.16   
177   $177.00    0.413625275   $73.21   
178   $178.00    0.411567438   $73.26   
179   $179.00    0.409519839   $73.30   
180   $180.00    0.407482427   $73.35   
181   $181.00    0.405455151   $73.39   
182   $182.00    0.403437961   $73.43   
183   $183.00    0.401430807   $73.46   
184   $184.00    0.399433639   $73.50   
185   $185.00    0.397446407   $73.53   
186   $186.00    0.395469062   $73.56   
187   $187.00    0.393501554   $73.58   
188   $188.00    0.391543835   $73.61   
189   $189.00    0.389595855   $73.63   
190   $190.00    0.387657567   $73.65   
191   $191.00    0.385728923   $73.67   
192   $192.00    0.383809873   $73.69   
193   $193.00    0.381900372   $73.71   
194   $194.00    0.38000037   $73.72   
195   $195.00    0.378109821   $73.73   
196   $196.00    0.376228677   $73.74   
197   $197.00    0.374356893   $73.75   
198   $198.00    0.372494421   $73.75   
199   $199.00    0.370641215   $73.76   
200   $200.00    0.368797229   $73.76   
201   $201.00    0.366962416   $73.76   
202   $202.00    0.365136733   $73.76   
203   $203.00    0.363320132   $73.75   
204   $204.00    0.361512569   $73.75   
205   $205.00    0.359713999   $73.74   
206   $206.00    0.357924377   $73.73   
207   $207.00    0.356143659   $73.72   
208   $208.00    0.3543718   $73.71   
209   $209.00    0.352608756   $73.70   
210   $210.00    0.350854484   $73.68   
211   $211.00    0.349108939   $73.66   
212   $212.00    0.347372079   $73.64   
213   $213.00    0.345643859   $73.62   
214   $214.00    0.343924238   $73.60   
215   $215.00    0.342213172   $73.58   
216   $216.00    0.340510619   $73.55   
217   $217.00    0.338816537   $73.52   
218   $218.00    0.337130882   $73.49   
219   $219.00    0.335453614   $73.46   
220   $220.00    0.333784691   $73.43   
221   $221.00    0.33212407   $73.40   
222   $222.00    0.330471712   $73.36   
223   $223.00    0.328827574   $73.33   
224   $224.00    0.327191616   $73.29   
225   $225.00    0.325563797   $73.25   
226   $226.00    0.323944076   $73.21   
227   $227.00    0.322332414   $73.17   
228   $228.00    0.320728771   $73.13   
229   $229.00    0.319133105   $73.08   
230   $230.00    0.317545378   $73.04   
231   $231.00    0.31596555   $72.99   
232   $232.00    0.314393582   $72.94   
233   $233.00    0.312829435   $72.89   
234   $234.00    0.31127307   $72.84   
235   $235.00    0.309724448   $72.79   
236   $236.00    0.30818353   $72.73   
237   $237.00    0.306650279   $72.68   
238   $238.00    0.305124655   $72.62   
239   $239.00    0.303606622   $72.56   
240   $240.00    0.302096142   $72.50   
241   $241.00    0.300593176   $72.44   
242   $242.00    0.299097687   $72.38   
243   $243.00    0.297609639   $72.32   
244   $244.00    0.296128994   $72.26   
245   $245.00    0.294655716   $72.19   
246   $246.00    0.293189767   $72.12   
247   $247.00    0.291731111   $72.06   
248   $248.00    0.290279713   $71.99   
249   $249.00    0.288835535   $71.92   
250   $250.00    0.287398542   $71.85   
251   $251.00    0.285968699   $71.78   
252   $252.00    0.284545969   $71.71   
253   $253.00    0.283130317   $71.63   
254   $254.00    0.281721709   $71.56   
255   $255.00    0.280320108   $71.48   
256   $256.00    0.278925481   $71.40   
257   $257.00    0.277537792   $71.33   
258   $258.00    0.276157007   $71.25   
259   $259.00    0.274783091   $71.17   
260   $260.00    0.273416011   $71.09   
261   $261.00    0.272055733   $71.01   
262   $262.00    0.270702222   $70.92   
263   $263.00    0.269355444   $70.84   
264   $264.00    0.268015367   $70.76   
265   $265.00    0.266681958   $70.67   
266   $266.00    0.265355182   $70.58   
267   $267.00    0.264035007   $70.50   
268   $268.00    0.2627214   $70.41   
269   $269.00    0.261414328   $70.32   
270   $270.00    0.260113759   $70.23   
271   $271.00    0.258819661   $70.14   
272   $272.00    0.257532001   $70.05   
273   $273.00    0.256250747   $69.96   
274   $274.00    0.254975868   $69.86   
275   $275.00    0.253707331   $69.77   
276   $276.00    0.252445106   $69.67   
277   $277.00    0.25118916   $69.58   
278   $278.00    0.249939463   $69.48   
279   $279.00    0.248695983   $69.39   
280   $280.00    0.247458689   $69.29   
281   $281.00    0.246227551   $69.19   
282   $282.00    0.245002539   $69.09   
283   $283.00    0.243783621   $68.99   
284   $284.00    0.242570767   $68.89   
285   $285.00    0.241363947   $68.79   
286   $286.00    0.240163131   $68.69   
287   $287.00    0.23896829   $68.58   
288   $288.00    0.237779393   $68.48   
289   $289.00    0.236596411   $68.38   
290   $290.00    0.235419314   $68.27   
291   $291.00    0.234248074   $68.17   
292   $292.00    0.233082661   $68.06   
293   $293.00    0.231923046   $67.95   
294   $294.00    0.2307692   $67.85   
295   $295.00    0.229621094   $67.74   
296   $296.00    0.228478701   $67.63   
297   $297.00    0.227341991   $67.52   
298   $298.00    0.226210936   $67.41   
299   $299.00    0.225085508   $67.30   
300   $300.00    0.22396568   $67.19   
301   $301.00    0.222851423   $67.08   
302   $302.00    0.221742709   $66.97   
303   $303.00    0.220639512   $66.85   
304   $304.00    0.219541803   $66.74   
305   $305.00    0.218449555   $66.63   
306   $306.00    0.217362741   $66.51   
307   $307.00    0.216281335   $66.40   
308   $308.00    0.215205308   $66.28   
309   $309.00    0.214134635   $66.17   
310   $310.00    0.213069288   $66.05   
311   $311.00    0.212009242   $65.93   
312   $312.00    0.21095447   $65.82   
313   $313.00    0.209904945   $65.70   
314   $314.00    0.208860642   $65.58   
315   $315.00    0.207821534   $65.46   
316   $316.00    0.206787596   $65.34   
317   $317.00    0.205758802   $65.23   
318   $318.00    0.204735127   $65.11   
319   $319.00    0.203716544   $64.99   
320   $320.00    0.202703029   $64.86   
321   $321.00    0.201694556   $64.74   
322   $322.00    0.2006911   $64.62   
323   $323.00    0.199692637   $64.50   
324   $324.00    0.198699142   $64.38   
325   $325.00    0.197710589   $64.26   
326   $326.00    0.196726954   $64.13   
327   $327.00    0.195748213   $64.01   
328   $328.00    0.194774341   $63.89   
329   $329.00    0.193805315   $63.76   
330   $330.00    0.192841109   $63.64   
331   $331.00    0.1918817   $63.51   
332   $332.00    0.190927065   $63.39   
333   $333.00    0.189977179   $63.26   
334   $334.00    0.189032019   $63.14   
335   $335.00    0.188091561   $63.01   
336   $336.00    0.187155782   $62.88   
337   $337.00    0.186224659   $62.76   
338   $338.00    0.185298168   $62.63   
339   $339.00    0.184376287   $62.50   
340   $340.00    0.183458992   $62.38   
341   $341.00    0.182546261   $62.25   
342   $342.00    0.18163807   $62.12   
343   $343.00    0.180734398   $61.99   
344   $344.00    0.179835222   $61.86   
345   $345.00    0.17894052   $61.73   
346   $346.00    0.178050268   $61.61   
347   $347.00    0.177164446   $61.48   
348   $348.00    0.176283031   $61.35   
349   $349.00    0.175406001   $61.22   
350   $350.00    0.174533334   $61.09   
351   $351.00    0.173665009   $60.96   
352   $352.00    0.172801004   $60.83   
353   $353.00    0.171941298   $60.70   
354   $354.00    0.171085868   $60.56   
355   $355.00    0.170234695   $60.43   
356   $356.00    0.169387756   $60.30   
357   $357.00    0.168545031   $60.17   
358   $358.00    0.167706498   $60.04   
359   $359.00    0.166872138   $59.91   
360   $360.00    0.166041928   $59.78   
361   $361.00    0.165215849   $59.64   
362   $362.00    0.164393879   $59.51   
363   $363.00    0.163575999   $59.38   
364   $364.00    0.162762188   $59.25   
365   $365.00    0.161952426   $59.11   
366   $366.00    0.161146693   $58.98   
367   $367.00    0.160344968   $58.85   
368   $368.00    0.159547232   $58.71   
369   $369.00    0.158753465   $58.58   
370   $370.00    0.157963646   $58.45   
371   $371.00    0.157177758   $58.31   
372   $372.00    0.156395779   $58.18   
373   $373.00    0.15561769   $58.05   
374   $374.00    0.154843473   $57.91   
375   $375.00    0.154073107   $57.78   
376   $376.00    0.153306574   $57.64   
377   $377.00    0.152543855   $57.51   
378   $378.00    0.15178493   $57.37   
379   $379.00    0.151029782   $57.24   
380   $380.00    0.15027839   $57.11   
381   $381.00    0.149530736   $56.97   
382   $382.00    0.148786802   $56.84   
383   $383.00    0.148046569   $56.70   
384   $384.00    0.147310019   $56.57   
385   $385.00    0.146577133   $56.43   
386   $386.00    0.145847894   $56.30   
387   $387.00    0.145122282   $56.16   
388   $388.00    0.144400281   $56.03   
389   $389.00    0.143681872   $55.89   
390   $390.00    0.142967036   $55.76   
391   $391.00    0.142255758   $55.62   
392   $392.00    0.141548018   $55.49   
393   $393.00    0.140843799   $55.35   
394   $394.00    0.140143083   $55.22   
395   $395.00    0.139445854   $55.08   
396   $396.00    0.138752093   $54.95   
397   $397.00    0.138061785   $54.81   
398   $398.00    0.13737491   $54.68   
399   $399.00    0.136691453   $54.54   
400   $400.00    0.136011396   $54.40   
401   $401.00    0.135334722   $54.27   
402   $402.00    0.134661415   $54.13   
403   $403.00    0.133991458   $54.00   
404   $404.00    0.133324834   $53.86   
405   $405.00    0.132661526   $53.73   
406   $406.00    0.132001518   $53.59   
407   $407.00    0.131344794   $53.46   
408   $408.00    0.130691338   $53.32   
409   $409.00    0.130041132   $53.19   
410   $410.00    0.129394161   $53.05   
411   $411.00    0.128750409   $52.92   
412   $412.00    0.12810986   $52.78   
413   $413.00    0.127472497   $52.65   
414   $414.00    0.126838306   $52.51   
415   $415.00    0.12620727   $52.38   
416   $416.00    0.125579373   $52.24   
417   $417.00    0.1249546   $52.11   
418   $418.00    0.124332935   $51.97   
419   $419.00    0.123714363   $51.84   
420   $420.00    0.123098869   $51.70   
421   $421.00    0.122486437   $51.57   
422   $422.00    0.121877051   $51.43   
423   $423.00    0.121270698   $51.30   
424   $424.00    0.120667361   $51.16   
425   $425.00    0.120067026   $51.03   
426   $426.00    0.119469678   $50.89   
427   $427.00    0.118875301   $50.76   
428   $428.00    0.118283882   $50.63   
429   $429.00    0.117695405   $50.49   
430   $430.00    0.117109855   $50.36   
431   $431.00    0.116527219   $50.22   
432   $432.00    0.115947482   $50.09   
433   $433.00    0.115370629   $49.96   
434   $434.00    0.114796646   $49.82   
435   $435.00    0.114225518   $49.69   
436   $436.00    0.113657232   $49.55   
437   $437.00    0.113091773   $49.42   
438   $438.00    0.112529127   $49.29   
439   $439.00    0.111969281   $49.15   
440   $440.00    0.11141222   $49.02   
441   $441.00    0.11085793   $48.89   
442   $442.00    0.110306398   $48.76   
443   $443.00    0.10975761   $48.62   
444   $444.00    0.109211552   $48.49   
445   $445.00    0.108668211   $48.36   
446   $446.00    0.108127573   $48.22   
447   $447.00    0.107589625   $48.09   
448   $448.00    0.107054353   $47.96   
449   $449.00    0.106521745   $47.83   
450   $450.00    0.105991786   $47.70   
451   $451.00    0.105464464   $47.56   
452   $452.00    0.104939765   $47.43   
453   $453.00    0.104417676   $47.30   
454   $454.00    0.103898185   $47.17   
455   $455.00    0.103381279   $47.04   
456   $456.00    0.102866944   $46.91   
457   $457.00    0.102355168   $46.78   
458   $458.00    0.101845939   $46.65   
459   $459.00    0.101339243   $46.51   
460   $460.00    0.100835067   $46.38   
461   $461.00    0.1003334   $46.25   
462   $462.00    0.099834229   $46.12   
463   $463.00    0.099337541   $45.99   
464   $464.00    0.098843325   $45.86   
465   $465.00    0.098351567   $45.73   
466   $466.00    0.097862256   $45.60   
467   $467.00    0.097375379   $45.47   
468   $468.00    0.096890924   $45.34   
469   $469.00    0.09640888   $45.22   
470   $470.00    0.095929234   $45.09   
471   $471.00    0.095451974   $44.96   
472   $472.00    0.094977088   $44.83   
473   $473.00    0.094504565   $44.70   
474   $474.00    0.094034393   $44.57   
475   $475.00    0.093566561   $44.44   
476   $476.00    0.093101055   $44.32   
477   $477.00    0.092637866   $44.19   
478   $478.00    0.092176981   $44.06   
479   $479.00    0.091718389   $43.93   
480   $480.00    0.091262079   $43.81   
481   $481.00    0.090808039   $43.68   
482   $482.00    0.090356257   $43.55   
483   $483.00    0.089906724   $43.42   
484   $484.00    0.089459427   $43.30   
485   $485.00    0.089014355   $43.17   
486   $486.00    0.088571497   $43.05   
487   $487.00    0.088130843   $42.92   
488   $488.00    0.087692381   $42.79   
489   $489.00    0.087256101   $42.67   
490   $490.00    0.086821991   $42.54   
491   $491.00    0.08639004   $42.42   
492   $492.00    0.085960239   $42.29   
493   $493.00    0.085532576   $42.17   
494   $494.00    0.085107041   $42.04   
495   $495.00    0.084683623   $41.92   
496   $496.00    0.084262312   $41.79   
497   $497.00    0.083843096   $41.67   
498   $498.00    0.083425966   $41.55   
499   $499.00    0.083010912   $41.42   
500   $500.00    0.082597922   $41.30   
              
           " $28,619.77 "   VALUE


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