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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)
2. Example : Loan amount (P)
(Next example)

1. Example : Find Monthly payment (A)


1. Find Monthly payment A = ?
for Loan amount P = 12000, Interest rate i = 5, Loan term n = 10 years,

Solution:
`P=12000` (Loan amount)

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

`n=10` years (Number of periods)

`"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)`

`=(12000*0.004167)/(1-(1+0.004167)^-120)`

`=(50)/(1-(1.0042)^-120)`

`=127.2786`

Create Amortization Schedule
Month = 1
`12000*0.004167=50`

`127.2786-50=77.2786`

`12000-77.2786=11922.7214`

Month = 2
`11922.7214*0.004167=49.678`

`127.2786-49.678=77.6006`

`11922.7214-77.6006=11845.1208`


Amortization table
MonthDatePrincipalInterestPaymentTotal Interest PaidTotal Remaining Balance
012000
1Mar-202477.278650127.27865011922.7214
2Apr-202477.600649.678127.278699.67811845.1208
3May-202477.923949.3547127.2786149.032711767.1969
4Jun-202478.248649.03127.2786198.062711688.9483
5Jul-202478.574648.704127.2786246.766711610.3737
6Aug-202478.90248.3766127.2786295.143311531.4717
7Sep-202479.230848.0478127.2786343.191111452.2409
8Oct-202479.560947.7177127.2786390.908811372.68
9Nov-202479.892447.3862127.2786438.29511292.7876
10Dec-202480.225347.0533127.2786485.348311212.5623
11Jan-202580.559646.719127.2786532.067311132.0027
12Feb-202580.895346.3833127.2786578.450611051.1074
13Mar-202581.232346.0463127.2786624.496910969.8751
14Apr-202581.570845.7078127.2786670.204710888.3043
15May-202581.910745.3679127.2786715.572610806.3936
16Jun-202582.25245.0266127.2786760.599210724.1416
17Jul-202582.594744.6839127.2786805.283110641.5469
18Aug-202582.938844.3398127.2786849.622910558.6081
19Sep-202583.284443.9942127.2786893.617110475.3237
20Oct-202583.631443.6472127.2786937.264310391.6923
21Nov-202583.979943.2987127.2786980.56310307.7124
22Dec-202584.329842.9488127.27861023.511810223.3826
23Jan-202684.681242.5974127.27861066.109210138.7014
24Feb-202685.03442.2446127.27861108.353810053.6674
25Mar-202685.388341.8903127.27861150.24419968.2791
26Apr-202685.744141.5345127.27861191.77869882.535
27May-202686.101441.1772127.27861232.95589796.4336
28Jun-202686.460140.8185127.27861273.77439709.9735
29Jul-202686.820440.4582127.27861314.23259623.1531
30Aug-202687.182140.0965127.27861354.3299535.971
31Sep-202687.545439.7332127.27861394.06229448.4256
32Oct-202687.910239.3684127.27861433.43069360.5154
33Nov-202688.276539.0021127.27861472.43279272.2389
34Dec-202688.644338.6343127.27861511.0679183.5946
35Jan-202789.013638.265127.27861549.3329094.581
36Feb-202789.384537.8941127.27861587.22619005.1965
37Mar-202789.756937.5217127.27861624.74788915.4396
38Apr-202790.130937.1477127.27861661.89558825.3087
39May-202790.506536.7721127.27861698.66768734.8022
40Jun-202790.883636.395127.27861735.06268643.9186
41Jul-202791.262336.0163127.27861771.07898552.6563
42Aug-202791.642535.6361127.27861806.7158461.0138
43Sep-202792.024435.2542127.27861841.96928368.9894
44Oct-202792.407834.8708127.27861876.848276.5816
45Nov-202792.792834.4858127.27861911.32588183.7888
46Dec-202793.179534.0991127.27861945.42498090.6093
47Jan-202893.567733.7109127.27861979.13587997.0416
48Feb-202893.957633.321127.27862012.45687903.084
49Mar-202894.349132.9295127.27862045.38637808.7349
50Apr-202894.742232.5364127.27862077.92277713.9927
51May-202895.13732.1416127.27862110.06437618.8557
52Jun-202895.533431.7452127.27862141.80957523.3223
53Jul-202895.931431.3472127.27862173.15677427.3909
54Aug-202896.331130.9475127.27862204.10427331.0598
55Sep-202896.732530.5461127.27862234.65037234.3273
56Oct-202897.135630.143127.27862264.79337137.1917
57Nov-202897.540329.7383127.27862294.53167039.6514
58Dec-202897.946729.3319127.27862323.86356941.7047
59Jan-202998.354828.9238127.27862352.78736843.3499
60Feb-202998.764628.514127.27862381.30136744.5853
61Mar-202999.176228.1024127.27862409.40376645.4091
62Apr-202999.589427.6892127.27862437.09296545.8197
63May-2029100.004427.2742127.27862464.36716445.8153
64Jun-2029100.42126.8576127.27862491.22476345.3943
65Jul-2029100.839526.4391127.27862517.66386244.5548
66Aug-2029101.259626.019127.27862543.68286143.2952
67Sep-2029101.681525.5971127.27862569.27996041.6137
68Oct-2029102.105225.1734127.27862594.45335939.5085
69Nov-2029102.530624.748127.27862619.20135836.9779
70Dec-2029102.957924.3207127.27862643.5225734.02
71Jan-2030103.386823.8918127.27862667.41385630.6332
72Feb-2030103.817623.461127.27862690.87485526.8156
73Mar-2030104.250223.0284127.27862713.90325422.5654
74Apr-2030104.684622.594127.27862736.49725317.8808
75May-2030105.120822.1578127.27862758.6555212.76
76Jun-2030105.558821.7198127.27862780.37485107.2012
77Jul-2030105.998621.28127.27862801.65485001.2026
78Aug-2030106.440320.8383127.27862822.49314894.7623
79Sep-2030106.883820.3948127.27862842.88794787.8785
80Oct-2030107.329119.9495127.27862862.83744680.5494
81Nov-2030107.776319.5023127.27862882.33974572.7731
82Dec-2030108.225419.0532127.27862901.39294464.5477
83Jan-2031108.676318.6023127.27862919.99524355.8714
84Feb-2031109.129118.1495127.27862938.14474246.7423
85Mar-2031109.583817.6948127.27862955.83954137.1585
86Apr-2031110.040417.2382127.27862973.07774027.1181
87May-2031110.498916.7797127.27862989.85743916.6192
88Jun-2031110.959416.3192127.27863006.17663805.6598
89Jul-2031111.421715.8569127.27863022.03353694.2381
90Aug-2031111.885915.3927127.27863037.42623582.3522
91Sep-2031112.352114.9265127.27863052.35273470.0001
92Oct-2031112.820314.4583127.27863066.8113357.1798
93Nov-2031113.290413.9882127.27863080.79923243.8894
94Dec-2031113.762413.5162127.27863094.31543130.127
95Jan-2032114.236413.0422127.27863107.35763015.8906
96Feb-2032114.712412.5662127.27863119.92382901.1782
97Mar-2032115.190412.0882127.27863132.0122785.9878
98Apr-2032115.670311.6083127.27863143.62032670.3175
99May-2032116.152311.1263127.27863154.74662554.1652
100Jun-2032116.636210.6424127.27863165.3892437.529
101Jul-2032117.122210.1564127.27863175.54542320.4068
102Aug-2032117.61029.6684127.27863185.21382202.7966
103Sep-2032118.10039.1783127.27863194.39212084.6963
104Oct-2032118.59248.6862127.27863203.07831966.1039
105Nov-2032119.08658.1921127.27863211.27041847.0174
106Dec-2032119.58277.6959127.27863218.96631727.4347
107Jan-2033120.0817.1976127.27863226.16391607.3537
108Feb-2033120.58136.6973127.27863232.86121486.7724
109Mar-2033121.08376.1949127.27863239.05611365.6887
110Apr-2033121.58825.6904127.27863244.74651244.1005
111May-2033122.09485.1838127.27863249.93031122.0057
112Jun-2033122.60364.675127.27863254.6053999.4021
113Jul-2033123.11444.1642127.27863258.7695876.2877
114Aug-2033123.62743.6512127.27863262.4207752.6603
115Sep-2033124.14253.1361127.27863265.5568628.5178
116Oct-2033124.65982.6188127.27863268.1756503.858
117Nov-2033125.17922.0994127.27863270.275378.6788
118Dec-2033125.70081.5778127.27863271.8528252.978
119Jan-2034126.22451.0541127.27863272.9069126.7535
120Feb-2034126.75350.5281127.28163273.4350
2. Find Monthly payment A = ?
for Loan amount P = 100000, Interest rate i = 15, Loan term n = 5 years,

Solution:
`P=100000` (Loan amount)

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

`n=5` years (Number of periods)

`"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)`

`=(100000*0.0125)/(1-(1+0.0125)^-60)`

`=(1250)/(1-(1.0125)^-60)`

`=2378.993`

Create Amortization Schedule
Month = 1
`100000*0.0125=1250`

`2378.993-1250=1128.993`

`100000-1128.993=98871.007`

Month = 2
`98871.007*0.0125=1235.8876`

`2378.993-1235.8876=1143.1054`

`98871.007-1143.1054=97727.9016`


Amortization table
MonthDatePrincipalInterestPaymentTotal Interest PaidTotal Remaining Balance
0100000
1Mar-20241128.99312502378.993125098871.007
2Apr-20241143.10541235.88762378.9932485.887697727.9016
3May-20241157.39421221.59882378.9933707.486496570.5074
4Jun-20241171.86171207.13132378.9934914.617795398.6457
5Jul-20241186.50991192.48312378.9936107.100894212.1358
6Aug-20241201.34131177.65172378.9937284.752593010.7945
7Sep-20241216.35811162.63492378.9938447.387491794.4364
8Oct-20241231.56251147.43052378.9939594.817990562.8739
9Nov-20241246.95711132.03592378.99310726.853889315.9168
10Dec-20241262.5441116.4492378.99311843.302888053.3728
11Jan-20251278.32581100.66722378.99312943.9786775.047
12Feb-20251294.30491084.68812378.99314028.658185480.7421
13Mar-20251310.48371068.50932378.99315097.167484170.2584
14Apr-20251326.86481052.12822378.99316149.295682843.3936
15May-20251343.45061035.54242378.99317184.83881499.943
16Jun-20251360.24371018.74932378.99318203.587380139.6993
17Jul-20251377.24681001.74622378.99319205.333578762.4525
18Aug-20251394.4623984.53072378.99320189.864277367.9902
19Sep-20251411.8931967.09992378.99321156.964175956.0971
20Oct-20251429.5418949.45122378.99322106.415374526.5553
21Nov-20251447.4111931.58192378.99323037.997273079.1442
22Dec-20251465.5037913.48932378.99323951.486571613.6405
23Jan-20261483.8225895.17052378.99324846.65770129.818
24Feb-20261502.3703876.62272378.99325723.279768627.4477
25Mar-20261521.1499857.84312378.99326581.122867106.2978
26Apr-20261540.1643838.82872378.99327419.951565566.1335
27May-20261559.4163819.57672378.99328239.528264006.7172
28Jun-20261578.909800.0842378.99329039.612262427.8082
29Jul-20261598.6454780.34762378.99329819.959860829.1628
30Aug-20261618.6285760.36452378.99330580.324359210.5343
31Sep-20261638.8613740.13172378.99331320.45657571.673
32Oct-20261659.3471719.64592378.99332040.101955912.3259
33Nov-20261680.0889698.90412378.99332739.00654232.237
34Dec-20261701.09677.9032378.99333416.90952531.147
35Jan-20271722.3537656.63932378.99334073.548350808.7933
36Feb-20271743.8831635.10992378.99334708.658249064.9102
37Mar-20271765.6816613.31142378.99335321.969647299.2286
38Apr-20271787.7526591.24042378.99335913.2145511.476
39May-20271810.0996568.89342378.99336482.103443701.3764
40Jun-20271832.7258546.26722378.99337028.370641868.6506
41Jul-20271855.6349523.35812378.99337551.728740013.0157
42Aug-20271878.8303500.16272378.99338051.891438134.1854
43Sep-20271902.3157476.67732378.99338528.568736231.8697
44Oct-20271926.0946452.89842378.99338981.467134305.7751
45Nov-20271950.1708428.82222378.99339410.289332355.6043
46Dec-20271974.5479404.44512378.99339814.734430381.0564
47Jan-20281999.2298379.76322378.99340194.497628381.8266
48Feb-20282024.2202354.77282378.99340549.270426357.6064
49Mar-20282049.5229329.47012378.99340878.740524308.0835
50Apr-20282075.142303.8512378.99341182.591522232.9415
51May-20282101.0812277.91182378.99341460.503320131.8603
52Jun-20282127.3447251.64832378.99341712.151618004.5156
53Jul-20282153.9366225.05642378.99341937.20815850.579
54Aug-20282180.8608198.13222378.99342135.340213669.7182
55Sep-20282208.1215170.87152378.99342306.211711461.5967
56Oct-20282235.723143.272378.99342449.48179225.8737
57Nov-20282263.6696115.32342378.99342564.80516962.2041
58Dec-20282291.965487.02762378.99342651.83274670.2387
59Jan-20292320.61558.3782378.99342710.21072349.6237
60Feb-20292349.623729.37032378.99442739.5810
3. Find Monthly payment A = ?
for Loan amount P = 20000, Interest rate i = 10, Loan term n = 4 years,

Solution:
`P=20000` (Loan amount)

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

`n=4` years (Number of periods)

`"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)`

`=(20000*0.008333)/(1-(1+0.008333)^-48)`

`=(166.6667)/(1-(1.0083)^-48)`

`=507.2517`

Create Amortization Schedule
Month = 1
`20000*0.008333=166.6667`

`507.2517-166.6667=340.585`

`20000-340.585=19659.415`

Month = 2
`19659.415*0.008333=163.8285`

`507.2517-163.8285=343.4232`

`19659.415-343.4232=19315.9918`


Amortization table
MonthDatePrincipalInterestPaymentTotal Interest PaidTotal Remaining Balance
020000
1Mar-2024340.585166.6667507.2517166.666719659.415
2Apr-2024343.4232163.8285507.2517330.495219315.9918
3May-2024346.2851160.9666507.2517491.461818969.7067
4Jun-2024349.1708158.0809507.2517649.542718620.5359
5Jul-2024352.0806155.1711507.2517804.713818268.4553
6Aug-2024355.0146152.2371507.2517956.950917913.4407
7Sep-2024357.973149.2787507.25171106.229617555.4677
8Oct-2024360.9561146.2956507.25171252.525217194.5116
9Nov-2024363.9641143.2876507.25171395.812816830.5475
10Dec-2024366.9971140.2546507.25171536.067416463.5504
11Jan-2025370.0554137.1963507.25171673.263716093.495
12Feb-2025373.1392134.1125507.25171807.376215720.3558
13Mar-2025376.2487131.003507.25171938.379215344.1071
14Apr-2025379.3841127.8676507.25172066.246814964.723
15May-2025382.5457124.706507.25172190.952814582.1773
16Jun-2025385.7336121.5181507.25172312.470914196.4437
17Jul-2025388.948118.3037507.25172430.774613807.4957
18Aug-2025392.1892115.0625507.25172545.837113415.3065
19Sep-2025395.4575111.7942507.25172657.631313019.849
20Oct-2025398.753108.4987507.25172766.1312621.096
21Nov-2025402.0759105.1758507.25172871.305812219.0201
22Dec-2025405.4265101.8252507.25172973.13111813.5936
23Jan-2026408.805198.4466507.25173071.577611404.7885
24Feb-2026412.211895.0399507.25173166.617510992.5767
25Mar-2026415.646991.6048507.25173258.222310576.9298
26Apr-2026419.110688.1411507.25173346.363410157.8192
27May-2026422.603284.6485507.25173431.01199735.216
28Jun-2026426.124981.1268507.25173512.13879309.0911
29Jul-2026429.675977.5758507.25173589.71458879.4152
30Aug-2026433.256673.9951507.25173663.70968446.1586
31Sep-2026436.86770.3847507.25173734.09438009.2916
32Oct-2026440.507666.7441507.25173800.83847568.784
33Nov-2026444.178563.0732507.25173863.91167124.6055
34Dec-2026447.8859.3717507.25173923.28336676.7255
35Jan-2027451.612355.6394507.25173978.92276225.1132
36Feb-2027455.375851.8759507.25174030.79865769.7374
37Mar-2027459.170648.0811507.25174078.87975310.5668
38Apr-2027462.99744.2547507.25174123.13444847.5698
39May-2027466.855340.3964507.25174163.53084380.7145
40Jun-2027470.745736.506507.25174200.03683909.9688
41Jul-2027474.668632.5831507.25174232.61993435.3002
42Aug-2027478.624228.6275507.25174261.24742956.676
43Sep-2027482.612724.639507.25174285.88642474.0633
44Oct-2027486.634520.6172507.25174306.50361987.4288
45Nov-2027490.689816.5619507.25174323.06551496.739
46Dec-2027494.778912.4728507.25174335.53831001.9601
47Jan-2028498.9028.3497507.25174343.888503.0581
48Feb-2028503.05814.1922507.25034348.08020


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2. Example : Loan amount (P)
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