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Home > Algebra calculators > Amortization example
Amortization example ( Enter your problem )
( Enter your problem )
  1. Example : Find Monthly payment (A)
  2. Example : Loan amount (P)
  3. Example : Find Interest rate (i)
  4. Example : Find Loan term (n)
1. Example : Find Monthly payment (A)
(Previous example)		3. Example : Find Interest rate (i)
(Next example)

2. Example : Loan amount (P)


1. Find Loan amount P = ?
for Monthly payment A = 126.63, Interest rate i = 5, Loan term n = 10 years,

Solution:
`i=5%=0.05` per year (Interest rate)

`n=10` years (Number of periods)

Monthly Amount `A=126.63` per month

`"Monthly rate" = "Annual rate"/12`

`"Monthly rate" = 0.05/12`

`"Monthly rate" = 0.004167`

`n=10*12=120` months

`A=(P*i)/(1-(1+i)^-n)`

`:.126.63=(P*0.004167)/(1-(1+0.004167)^-120)`

`:.126.63=(P*0.004167)/(1-(1.0042)^-120)`

`:.126.63=(P*0.004167)/(1-0.6072)`

`:.126.63=(P*0.004167)/(0.3928)`

`:.P=126.63*0.3928/0.004167`

`:.P=11938.8474`

Create Amortization Schedule
Month = 1
`11938.8474*0.004167=49.7452`

`126.63-49.7452=76.8848`

`11938.8474-76.8848=11861.9626`

Month = 2
`11861.9626*0.004167=49.4248`

`126.63-49.4248=77.2052`

`11861.9626-77.2052=11784.7574`


Amortization table
MonthDatePrincipalInterestPaymentTotal Interest PaidTotal Remaining Balance
011938.8474
1Mar-202476.884849.7452126.6349.745211861.9626
2Apr-202477.205249.4248126.6399.1711784.7574
3May-202477.526849.1032126.63148.273211707.2306
4Jun-202477.849948.7801126.63197.053311629.3807
5Jul-202478.174248.4558126.63245.509111551.2065
6Aug-202478.548.13126.63293.639111472.7065
7Sep-202478.827147.8029126.63341.44211393.8794
8Oct-202479.155547.4745126.63388.916511314.7239
9Nov-202479.485347.1447126.63436.061211235.2386
10Dec-202479.816546.8135126.63482.874711155.4221
11Jan-202580.149146.4809126.63529.355611075.273
12Feb-202580.48346.147126.63575.502610994.79
13Mar-202580.818445.8116126.63621.314210913.9716
14Apr-202581.155145.4749126.63666.789110832.8165
15May-202581.493345.1367126.63711.925810751.3232
16Jun-202581.832844.7972126.63756.72310669.4904
17Jul-202582.173844.4562126.63801.179210587.3166
18Aug-202582.516244.1138126.63845.29310504.8004
19Sep-202582.8643.77126.63889.06310421.9404
20Oct-202583.205243.4248126.63932.487810338.7352
21Nov-202583.551943.0781126.63975.565910255.1833
22Dec-202583.900142.7299126.631018.295810171.2832
23Jan-202684.249742.3803126.631060.676110087.0335
24Feb-202684.600742.0293126.631102.705410002.4328
25Mar-202684.953241.6768126.631144.38229917.4796
26Apr-202685.307241.3228126.631185.7059832.1724
27May-202685.662640.9674126.631226.67249746.5098
28Jun-202686.019540.6105126.631267.28299660.4903
29Jul-202686.37840.252126.631307.53499574.1123
30Aug-202686.737939.8921126.631347.4279487.3744
31Sep-202687.099339.5307126.631386.95779400.2751
32Oct-202687.462239.1678126.631426.12559312.8129
33Nov-202687.826638.8034126.631464.92899224.9863
34Dec-202688.192638.4374126.631503.36639136.7937
35Jan-202788.5638.07126.631541.43639048.2337
36Feb-202788.92937.701126.631579.13738959.3047
37Mar-202789.299637.3304126.631616.46778870.0051
38Apr-202789.671636.9584126.631653.42618780.3335
39May-202790.045336.5847126.631690.01088690.2882
40Jun-202790.420536.2095126.631726.22038599.8677
41Jul-202790.797235.8328126.631762.05318509.0705
42Aug-202791.175535.4545126.631797.50768417.895
43Sep-202791.555435.0746126.631832.58228326.3396
44Oct-202791.936934.6931126.631867.27538234.4027
45Nov-202792.3234.31126.631901.58538142.0827
46Dec-202792.704733.9253126.631935.51068049.378
47Jan-202893.090933.5391126.631969.04977956.2871
48Feb-202893.478833.1512126.632002.20097862.8083
49Mar-202893.868332.7617126.632034.96267768.94
50Apr-202894.259432.3706126.632067.33327674.6806
51May-202894.652231.9778126.632099.3117580.0284
52Jun-202895.046531.5835126.632130.89457484.9819
53Jul-202895.442631.1874126.632162.08197389.5393
54Aug-202895.840330.7897126.632192.87167293.699
55Sep-202896.239630.3904126.632223.2627197.4594
56Oct-202896.640629.9894126.632253.25147100.8188
57Nov-202897.043329.5867126.632282.83817003.7755
58Dec-202897.447629.1824126.632312.02056906.3279
59Jan-202997.853628.7764126.632340.79696808.4743
60Feb-202998.261428.3686126.632369.16556710.2129
61Mar-202998.670827.9592126.632397.12476611.5421
62Apr-202999.081927.5481126.632424.67286512.4602
63May-202999.494727.1353126.632451.80816412.9655
64Jun-202999.909326.7207126.632478.52886313.0562
65Jul-2029100.325626.3044126.632504.83326212.7306
66Aug-2029100.743625.8864126.632530.71966111.987
67Sep-2029101.163425.4666126.632556.18626010.8236
68Oct-2029101.584925.0451126.632581.23135909.2387
69Nov-2029102.008224.6218126.632605.85315807.2305
70Dec-2029102.433224.1968126.632630.04995704.7973
71Jan-2030102.8623.77126.632653.81995601.9373
72Feb-2030103.288623.3414126.632677.16135498.6487
73Mar-2030103.71922.911126.632700.07235394.9297
74Apr-2030104.151122.4789126.632722.55125290.7786
75May-2030104.585122.0449126.632744.59615186.1935
76Jun-2030105.020921.6091126.632766.20525081.1726
77Jul-2030105.458421.1716126.632787.37684975.7142
78Aug-2030105.897920.7321126.632808.10894869.8163
79Sep-2030106.339120.2909126.632828.39984763.4772
80Oct-2030106.782219.8478126.632848.24764656.695
81Nov-2030107.227119.4029126.632867.65054549.4679
82Dec-2030107.673918.9561126.632886.60664441.794
83Jan-2031108.122518.5075126.632905.11414333.6715
84Feb-2031108.57318.057126.632923.17114225.0985
85Mar-2031109.025417.6046126.632940.77574116.0731
86Apr-2031109.479717.1503126.632957.9264006.5934
87May-2031109.935916.6941126.632974.62013896.6575
88Jun-2031110.393916.2361126.632990.85623786.2636
89Jul-2031110.853915.7761126.633006.63233675.4097
90Aug-2031111.315815.3142126.633021.94653564.0939
91Sep-2031111.779614.8504126.633036.79693452.3143
92Oct-2031112.245414.3846126.633051.18153340.0689
93Nov-2031112.71313.917126.633065.09853227.3559
94Dec-2031113.182713.4473126.633078.54583114.1732
95Jan-2032113.654312.9757126.633091.52153000.5189
96Feb-2032114.127812.5022126.633104.02372886.3911
97Mar-2032114.603412.0266126.633116.05032771.7877
98Apr-2032115.080911.5491126.633127.59942656.7068
99May-2032115.560411.0696126.633138.6692541.1464
100Jun-2032116.041910.5881126.633149.25712425.1045
101Jul-2032116.525410.1046126.633159.36172308.5791
102Aug-2032117.01099.6191126.633168.98082191.5682
103Sep-2032117.49859.1315126.633178.11232074.0697
104Oct-2032117.9888.642126.633186.75431956.0817
105Nov-2032118.47978.1503126.633194.90461837.602
106Dec-2032118.97337.6567126.633202.56131718.6287
107Jan-2033119.4697.161126.633209.72231599.1597
108Feb-2033119.96686.6632126.633216.38551479.1929
109Mar-2033120.46676.1633126.633222.54881358.7262
110Apr-2033120.96865.6614126.633228.21021237.7576
111May-2033121.47275.1573126.633233.36751116.2849
112Jun-2033121.97884.6512126.633238.0187994.3061
113Jul-2033122.48714.1429126.633242.1616871.819
114Aug-2033122.99743.6326126.633245.7942748.8216
115Sep-2033123.50993.1201126.633248.9143625.3117
116Oct-2033124.02452.6055126.633251.5198501.2872
117Nov-2033124.54132.0887126.633253.6085376.7459
118Dec-2033125.06021.5698126.633255.1783251.6857
119Jan-2034125.58131.0487126.633256.227126.1044
120Feb-2034126.10440.5254126.62983256.75240
2. Find Loan amount P = ?
for Monthly payment A = 2379, Interest rate i = 15, Loan term n = 5 years,

Solution:
`i=15%=0.15` per year (Interest rate)

`n=5` years (Number of periods)

Monthly Amount `A=2379` per month

`"Monthly rate" = "Annual rate"/12`

`"Monthly rate" = 0.15/12`

`"Monthly rate" = 0.0125`

`n=5*12=60` months

`A=(P*i)/(1-(1+i)^-n)`

`:.2379=(P*0.0125)/(1-(1+0.0125)^-60)`

`:.2379=(P*0.0125)/(1-(1.0125)^-60)`

`:.2379=(P*0.0125)/(1-0.4746)`

`:.2379=(P*0.0125)/(0.5254)`

`:.P=2379*0.5254/0.0125`

`:.P=100000.2939`

Create Amortization Schedule
Month = 1
`100000.2939*0.0125=1250.0037`

`2379-1250.0037=1128.9963`

`100000.2939-1128.9963=98871.2976`

Month = 2
`98871.2976*0.0125=1235.8912`

`2379-1235.8912=1143.1088`

`98871.2976-1143.1088=97728.1888`


Amortization table
MonthDatePrincipalInterestPaymentTotal Interest PaidTotal Remaining Balance
0100000.2939
1Mar-20241128.99631250.003723791250.003798871.2976
2Apr-20241143.10881235.891223792485.894997728.1888
3May-20241157.39761221.602423793707.497396570.7912
4Jun-20241171.86511207.134923794914.632295398.9261
5Jul-20241186.51341192.486623796107.118894212.4127
6Aug-20241201.34481177.655223797284.77493011.0679
7Sep-20241216.36171162.638323798447.412391794.7062
8Oct-20241231.56621147.433823799594.846190563.14
9Nov-20241246.96081132.0392237910726.885389316.1792
10Dec-20241262.54781116.4522237911843.337588053.6314
11Jan-20251278.32961100.6704237912944.007986775.3018
12Feb-20251294.30871084.6913237914028.699285480.9931
13Mar-20251310.48761068.5124237915097.211684170.5055
14Apr-20251326.86871052.1313237916149.342982843.6368
15May-20251343.45451035.5455237917184.888481500.1823
16Jun-20251360.24771018.7523237918203.640780139.9346
17Jul-20251377.25081001.7492237919205.389978762.6838
18Aug-20251394.4665984.5335237920189.923477368.2173
19Sep-20251411.8973967.1027237921157.026175956.32
20Oct-20251429.546949.454237922106.480174526.774
21Nov-20251447.4153931.5847237923038.064873079.3587
22Dec-20251465.508913.492237923951.556871613.8507
23Jan-20261483.8269895.1731237924846.729970130.0238
24Feb-20261502.3747876.6253237925723.355268627.6491
25Mar-20261521.1544857.8456237926581.200867106.4947
26Apr-20261540.1688838.8312237927420.03265566.3259
27May-20261559.4209819.5791237928239.611164006.905
28Jun-20261578.9137800.0863237929039.697462427.9913
29Jul-20261598.6501780.3499237929820.047360829.3412
30Aug-20261618.6332760.3668237930580.414159210.708
31Sep-20261638.8662740.1338237931320.547957571.8418
32Oct-20261659.352719.648237932040.195955912.4898
33Nov-20261680.0939698.9061237932739.10254232.3959
34Dec-20261701.0951677.9049237933417.006952531.3008
35Jan-20271722.3587656.6413237934073.648250808.9421
36Feb-20271743.8882635.1118237934708.7649065.0539
37Mar-20271765.6868613.3132237935322.073247299.3671
38Apr-20271787.7579591.2421237935913.315345511.6092
39May-20271810.1049568.8951237936482.210443701.5043
40Jun-20271832.7312546.2688237937028.479241868.7731
41Jul-20271855.6403523.3597237937551.838940013.1328
42Aug-20271878.8358500.1642237938052.003138134.297
43Sep-20271902.3213476.6787237938528.681836231.9757
44Oct-20271926.1003452.8997237938981.581534305.8754
45Nov-20271950.1766428.8234237939410.404932355.6988
46Dec-20271974.5538404.4462237939814.851130381.145
47Jan-20281999.2357379.7643237940194.615428381.9093
48Feb-20282024.2261354.7739237940549.389326357.6832
49Mar-20282049.529329.471237940878.860324308.1542
50Apr-20282075.1481303.8519237941182.712222233.0061
51May-20282101.0874277.9126237941460.624820131.9187
52Jun-20282127.351251.649237941712.273818004.5677
53Jul-20282153.9429225.0571237941937.330915850.6248
54Aug-20282180.8672198.1328237942135.463713669.7576
55Sep-20282208.128170.872237942306.335711461.6296
56Oct-20282235.7296143.2704237942449.60619225.9
57Nov-20282263.6762115.3238237942564.92996962.2238
58Dec-20282291.972287.0278237942651.95774670.2516
59Jan-20292320.621958.3781237942710.33582349.6297
60Feb-20292349.629729.37042379.000142739.70620
3. Find Loan amount P = ?
for Monthly payment A = 507.25, Interest rate i = 10, Loan term n = 4 years,

Solution:
`i=10%=0.1` per year (Interest rate)

`n=4` years (Number of periods)

Monthly Amount `A=507.25` per month

`"Monthly rate" = "Annual rate"/12`

`"Monthly rate" = 0.1/12`

`"Monthly rate" = 0.008333`

`n=4*12=48` months

`A=(P*i)/(1-(1+i)^-n)`

`:.507.25=(P*0.008333)/(1-(1+0.008333)^-48)`

`:.507.25=(P*0.008333)/(1-(1.0083)^-48)`

`:.507.25=(P*0.008333)/(1-0.6714)`

`:.507.25=(P*0.008333)/(0.3286)`

`:.P=507.25*0.3286/0.008333`

`:.P=19999.9342`

Create Amortization Schedule
Month = 1
`19999.9342*0.008333=166.6661`

`507.25-166.6661=340.5839`

`19999.9342-340.5839=19659.3503`

Month = 2
`19659.3503*0.008333=163.8279`

`507.25-163.8279=343.4221`

`19659.3503-343.4221=19315.9282`


Amortization table
MonthDatePrincipalInterestPaymentTotal Interest PaidTotal Remaining Balance
019999.9342
1Mar-2024340.5839166.6661507.25166.666119659.3503
2Apr-2024343.4221163.8279507.25330.49419315.9282
3May-2024346.2839160.9661507.25491.460118969.6443
4Jun-2024349.1696158.0804507.25649.540518620.4747
5Jul-2024352.0794155.1706507.25804.711118268.3953
6Aug-2024355.0134152.2366507.25956.947717913.3819
7Sep-2024357.9718149.2782507.251106.225917555.4101
8Oct-2024360.9549146.2951507.251252.52117194.4552
9Nov-2024363.9629143.2871507.251395.808116830.4923
10Dec-2024366.9959140.2541507.251536.062216463.4964
11Jan-2025370.0542137.1958507.251673.25816093.4422
12Feb-2025373.138134.112507.251807.3715720.3042
13Mar-2025376.2475131.0025507.251938.372515344.0567
14Apr-2025379.3829127.8671507.252066.239614964.6738
15May-2025382.5444124.7056507.252190.945214582.1294
16Jun-2025385.7323121.5177507.252312.462914196.3971
17Jul-2025388.9467118.3033507.252430.766213807.4504
18Aug-2025392.1879115.0621507.252545.828313415.2625
19Sep-2025395.4561111.7939507.252657.622213019.8064
20Oct-2025398.7516108.4984507.252766.120612621.0548
21Nov-2025402.0745105.1755507.252871.296112218.9803
22Dec-2025405.4252101.8248507.252973.120911813.5551
23Jan-2026408.803798.4463507.253071.567211404.7514
24Feb-2026412.210495.0396507.253166.606810992.541
25Mar-2026415.645591.6045507.253258.211310576.8955
26Apr-2026419.109288.1408507.253346.352110157.7863
27May-2026422.601884.6482507.253431.00039735.1845
28Jun-2026426.123581.1265507.253512.12689309.061
29Jul-2026429.674577.5755507.253589.70238879.3865
30Aug-2026433.255173.9949507.253663.69728446.1314
31Sep-2026436.865670.3844507.253734.08168009.2658
32Oct-2026440.506166.7439507.253800.82557568.7597
33Nov-2026444.17763.073507.253863.89857124.5827
34Dec-2026447.878559.3715507.253923.276676.7042
35Jan-2027451.610855.6392507.253978.90926225.0934
36Feb-2027455.374251.8758507.254030.7855769.7192
37Mar-2027459.16948.081507.254078.8665310.5502
38Apr-2027462.995444.2546507.254123.12064847.5548
39May-2027466.853740.3963507.254163.51694380.7011
40Jun-2027470.744236.5058507.254200.02273909.9569
41Jul-2027474.66732.583507.254232.60573435.2899
42Aug-2027478.622628.6274507.254261.23312956.6673
43Sep-2027482.611124.6389507.254285.8722474.0562
44Oct-2027486.632920.6171507.254306.48911987.4233
45Nov-2027490.688116.5619507.254323.0511496.7352
46Dec-2027494.777212.4728507.254335.52381001.958
47Jan-2028498.90048.3496507.254343.8734503.0576
48Feb-2028503.05764.1921507.24974348.06550


This material is intended as a summary. Use your textbook for detail explanation.
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1. Example : Find Monthly payment (A)
(Previous example)		3. Example : Find Interest rate (i)
(Next example)


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