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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)
3. Example : Find Interest rate (i)
(Previous example)

4. Example : Find Loan term (n)


1. Find Loan term n = ?
for Monthly payment A = 126.63, Loan amount P = 12000, Interest rate i = 5,

Solution:
`P=12000` (Loan amount)

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

Monthly Amount `A=126.63` per month

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

`"Monthly rate" = 0.05/12`

`"Monthly rate" = 0.004167`

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

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

`:.1-(1+0.004167)^-n=(12000*0.004167)/126.63`

`:.1-(1.0042)^-n=0.3949`

`:.(1.0042)^-n=1-0.3949`

`:.(1.0042)^-n=0.6051`

taking natural log on both the sides
`:.ln(1.0042)^-n=ln(0.6051)`

`:.-n*ln(1.0042)=ln(0.6051)`

`:.-n=ln(0.6051)/ln(1.0042)`

`:.-n=(-0.5023)/(0.0042)`

`:.-n=-120.7984`

`:.n=120.7984`

`:.n=121`

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

`126.63-50=76.63`

`12000-76.63=11923.37`

Month = 2
`11923.37*0.004167=49.6807`

`126.63-49.6807=76.9493`

`11923.37-76.9493=11846.4207`


Amortization table
MonthDatePrincipalInterestPaymentTotal Interest PaidTotal Remaining Balance
012000
1Mar-202476.6350126.635011923.37
2Apr-202476.949349.6807126.6399.680711846.4207
3May-202477.269949.3601126.63149.040811769.1508
4Jun-202477.591949.0381126.63198.078911691.5589
5Jul-202477.915248.7148126.63246.793711613.6437
6Aug-202478.239848.3902126.63295.183911535.4039
7Sep-202478.565848.0642126.63343.248111456.8381
8Oct-202478.893247.7368126.63390.984911377.9449
9Nov-202479.221947.4081126.63438.39311298.723
10Dec-202479.55247.078126.63485.47111219.171
11Jan-202579.883546.7465126.63532.217511139.2875
12Feb-202580.216346.4137126.63578.631211059.0712
13Mar-202580.550546.0795126.63624.710710978.5207
14Apr-202580.886245.7438126.63670.454510897.6345
15May-202581.223245.4068126.63715.861310816.4113
16Jun-202581.561645.0684126.63760.929710734.8497
17Jul-202581.901544.7285126.63805.658210652.9482
18Aug-202582.242744.3873126.63850.045510570.7055
19Sep-202582.585444.0446126.63894.090110488.1201
20Oct-202582.929543.7005126.63937.790610405.1906
21Nov-202583.27543.355126.63981.145610321.9156
22Dec-202583.62243.008126.631024.153610238.2936
23Jan-202683.970442.6596126.631066.813210154.3232
24Feb-202684.320342.3097126.631109.122910070.0029
25Mar-202684.671741.9583126.631151.08129985.3312
26Apr-202685.024541.6055126.631192.68679900.3067
27May-202685.378741.2513126.631233.9389814.928
28Jun-202685.734540.8955126.631274.83359729.1935
29Jul-202686.091740.5383126.631315.37189643.1018
30Aug-202686.450440.1796126.631355.55149556.6514
31Sep-202686.810639.8194126.631395.37089469.8408
32Oct-202687.172339.4577126.631434.82859382.6685
33Nov-202687.535539.0945126.631473.9239295.133
34Dec-202687.900338.7297126.631512.65279207.2327
35Jan-202788.266538.3635126.631551.01629118.9662
36Feb-202788.634337.9957126.631589.01199030.3319
37Mar-202789.003637.6264126.631626.63838941.3283
38Apr-202789.374537.2555126.631663.89388851.9538
39May-202789.746936.8831126.631700.77698762.2069
40Jun-202790.120836.5092126.631737.28618672.0861
41Jul-202790.496336.1337126.631773.41988581.5898
42Aug-202790.873435.7566126.631809.17648490.7164
43Sep-202791.25235.378126.631844.55448399.4644
44Oct-202791.632234.9978126.631879.55228307.8322
45Nov-202792.01434.616126.631914.16828215.8182
46Dec-202792.397434.2326126.631948.40088123.4208
47Jan-202892.782433.8476126.631982.24848030.6384
48Feb-202893.16933.461126.632015.70947937.4694
49Mar-202893.557233.0728126.632048.78227843.9122
50Apr-202893.94732.683126.632081.46527749.9652
51May-202894.338532.2915126.632113.75677655.6267
52Jun-202894.731631.8984126.632145.65517560.8951
53Jul-202895.126331.5037126.632177.15887465.7688
54Aug-202895.522631.1074126.632208.26627370.2462
55Sep-202895.920630.7094126.632238.97567274.3256
56Oct-202896.320330.3097126.632269.28537178.0053
57Nov-202896.721629.9084126.632299.19377081.2837
58Dec-202897.124729.5053126.632328.6996984.159
59Jan-202997.529329.1007126.632357.79976886.6297
60Feb-202997.935728.6943126.632386.4946788.694
61Mar-202998.343828.2862126.632414.78026690.3502
62Apr-202998.753527.8765126.632442.65676591.5967
63May-202999.16527.465126.632470.12176492.4317
64Jun-202999.578227.0518126.632497.17356392.8535
65Jul-202999.993126.6369126.632523.81046292.8604
66Aug-2029100.409726.2203126.632550.03076192.4507
67Sep-2029100.828125.8019126.632575.83266091.6226
68Oct-2029101.248225.3818126.632601.21445990.3744
69Nov-2029101.670124.9599126.632626.17435888.7043
70Dec-2029102.093724.5363126.632650.71065786.6106
71Jan-2030102.519124.1109126.632674.82155684.0915
72Feb-2030102.946323.6837126.632698.50525581.1452
73Mar-2030103.375223.2548126.632721.765477.77
74Apr-2030103.80622.824126.632744.5845373.964
75May-2030104.238522.3915126.632766.97555269.7255
76Jun-2030104.672821.9572126.632788.93275165.0527
77Jul-2030105.108921.5211126.632810.45385059.9438
78Aug-2030105.546921.0831126.632831.53694954.3969
79Sep-2030105.986720.6433126.632852.18024848.4102
80Oct-2030106.428320.2017126.632872.38194741.9819
81Nov-2030106.871719.7583126.632892.14024635.1102
82Dec-2030107.31719.313126.632911.45324527.7932
83Jan-2031107.764218.8658126.632930.3194420.029
84Feb-2031108.213218.4168126.632948.73584311.8158
85Mar-2031108.664117.9659126.632966.70174203.1517
86Apr-2031109.116917.5131126.632984.21484094.0348
87May-2031109.571517.0585126.633001.27333984.4633
88Jun-2031110.028116.6019126.633017.87523874.4352
89Jul-2031110.486516.1435126.633034.01873763.9487
90Aug-2031110.946915.6831126.633049.70183653.0018
91Sep-2031111.409215.2208126.633064.92263541.5926
92Oct-2031111.873414.7566126.633079.67923429.7192
93Nov-2031112.339514.2905126.633093.96973317.3797
94Dec-2031112.807613.8224126.633107.79213204.5721
95Jan-2032113.277613.3524126.633121.14453091.2945
96Feb-2032113.749612.8804126.633134.02492977.5449
97Mar-2032114.223612.4064126.633146.43132863.3213
98Apr-2032114.699511.9305126.633158.36182748.6218
99May-2032115.177411.4526126.633169.81442633.4444
100Jun-2032115.657310.9727126.633180.78712517.7871
101Jul-2032116.139210.4908126.633191.27792401.6479
102Aug-2032116.623110.0069126.633201.28482285.0248
103Sep-2032117.10919.5209126.633210.80572167.9157
104Oct-2032117.5979.033126.633219.83872050.3187
105Nov-2032118.0878.543126.633228.38171932.2317
106Dec-2032118.5798.051126.633236.43271813.6527
107Jan-2033119.07317.5569126.633243.98961694.5796
108Feb-2033119.56937.0607126.633251.05031575.0103
109Mar-2033120.06756.5625126.633257.61281454.9428
110Apr-2033120.56776.0623126.633263.67511334.3751
111May-2033121.07015.5599126.633269.2351213.305
112Jun-2033121.57465.0554126.633274.29041091.7304
113Jul-2033122.08114.5489126.633278.8393969.6493
114Aug-2033122.58984.0402126.633282.8795847.0595
115Sep-2033123.10063.5294126.633286.4089723.9589
116Oct-2033123.61353.0165126.633289.4254600.3454
117Nov-2033124.12862.5014126.633291.9268476.2168
118Dec-2033124.64581.9842126.633293.911351.571
119Jan-2034125.16511.4649126.633295.3759226.4059
120Feb-2034125.68660.9434126.633296.3193100.7193
121Mar-2034100.71930.4197101.1393296.7390
2. Find Loan term n = ?
for Monthly payment A = 2379, Loan amount P = 100000, Interest rate i = 15,

Solution:
`P=100000` (Loan amount)

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

Monthly Amount `A=2379` per month

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

`"Monthly rate" = 0.15/12`

`"Monthly rate" = 0.0125`

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

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

`:.1-(1+0.0125)^-n=(100000*0.0125)/2379`

`:.1-(1.0125)^-n=0.5254`

`:.(1.0125)^-n=1-0.5254`

`:.(1.0125)^-n=0.4746`

taking natural log on both the sides
`:.ln(1.0125)^-n=ln(0.4746)`

`:.-n*ln(1.0125)=ln(0.4746)`

`:.-n=ln(0.4746)/ln(1.0125)`

`:.-n=(-0.7453)/(0.0124)`

`:.-n=-59.9997`

`:.n=59.9997`

`:.n=60`

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

`2379-1250=1129`

`100000-1129=98871`

Month = 2
`98871*0.0125=1235.8875`

`2379-1235.8875=1143.1125`

`98871-1143.1125=97727.8875`


Amortization table
MonthDatePrincipalInterestPaymentTotal Interest PaidTotal Remaining Balance
0100000
1Mar-2024112912502379125098871
2Apr-20241143.11251235.887523792485.887597727.8875
3May-20241157.40141221.598623793707.486196570.4861
4Jun-20241171.86891207.131123794914.617295398.6172
5Jul-20241186.51731192.482723796107.099994212.0999
6Aug-20241201.34881177.651223797284.751193010.7511
7Sep-20241216.36561162.634423798447.385591794.3855
8Oct-20241231.57021147.429823799594.815390562.8153
9Nov-20241246.96481132.0352237910726.850589315.8505
10Dec-20241262.55191116.4481237911843.298688053.2986
11Jan-20251278.33381100.6662237912943.964886774.9648
12Feb-20251294.31291084.6871237914028.651985480.6519
13Mar-20251310.49191068.5081237915097.1684170.16
14Apr-20251326.8731052.127237916149.28782843.287
15May-20251343.45891035.5411237917184.828181499.8281
16Jun-20251360.25211018.7479237918203.57680139.576
17Jul-20251377.25531001.7447237919205.320778762.3207
18Aug-20251394.471984.529237920189.849777367.8497
19Sep-20251411.9019967.0981237921156.947875955.9478
20Oct-20251429.5507949.4493237922106.397174526.3971
21Nov-20251447.42931.58237923037.977173078.9771
22Dec-20251465.5128913.4872237923951.464371613.4643
23Jan-20261483.8317895.1683237924846.632670129.6326
24Feb-20261502.3796876.6204237925723.25368627.253
25Mar-20261521.1593857.8407237926581.093767106.0937
26Apr-20261540.1738838.8262237927419.919965565.9199
27May-20261559.426819.574237928239.493964006.4939
28Jun-20261578.9188800.0812237929039.575162427.5751
29Jul-20261598.6553780.3447237929819.919860828.9198
30Aug-20261618.6385760.3615237930580.281359210.2813
31Sep-20261638.8715740.1285237931320.409857571.4098
32Oct-20261659.3574719.6426237932040.052455912.0524
33Nov-20261680.0993698.9007237932738.953154231.9531
34Dec-20261701.1006677.8994237933416.852552530.8525
35Jan-20271722.3643656.6357237934073.488250808.4882
36Feb-20271743.8939635.1061237934708.594349064.5943
37Mar-20271765.6926613.3074237935321.901747298.9017
38Apr-20271787.7637591.2363237935913.13845511.138
39May-20271810.1108568.8892237936482.027243701.0272
40Jun-20271832.7372546.2628237937028.2941868.29
41Jul-20271855.6464523.3536237937551.643640012.6436
42Aug-20271878.842500.158237938051.801638133.8016
43Sep-20271902.3275476.6725237938528.474136231.4741
44Oct-20271926.1066452.8934237938981.367534305.3675
45Nov-20271950.1829428.8171237939410.184632355.1846
46Dec-20271974.5602404.4398237939814.624430380.6244
47Jan-20281999.2422379.7578237940194.382228381.3822
48Feb-20282024.2327354.7673237940549.149526357.1495
49Mar-20282049.5356329.4644237940878.613924307.6139
50Apr-20282075.1548303.8452237941182.459122232.4591
51May-20282101.0943277.9057237941460.364820131.3648
52Jun-20282127.3579251.6421237941712.006918004.0069
53Jul-20282153.9499225.0501237941937.05715850.057
54Aug-20282180.8743198.1257237942135.182713669.1827
55Sep-20282208.1352170.8648237942306.047511461.0475
56Oct-20282235.7369143.2631237942449.31069225.3106
57Nov-20282263.6836115.3164237942564.6276961.627
58Dec-20282291.979787.0203237942651.64734669.6473
59Jan-20292320.629458.3706237942710.01792349.0179
60Feb-20292349.017929.36272378.380642739.38060
3. Find Loan term n = ?
for Monthly payment A = 507.25, Loan amount P = 20000, Interest rate i = 10,

Solution:
`P=20000` (Loan amount)

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

Monthly Amount `A=507.25` per month

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

`"Monthly rate" = 0.1/12`

`"Monthly rate" = 0.008333`

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

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

`:.1-(1+0.008333)^-n=(20000*0.008333)/507.25`

`:.1-(1.0083)^-n=0.3286`

`:.(1.0083)^-n=1-0.3286`

`:.(1.0083)^-n=0.6714`

taking natural log on both the sides
`:.ln(1.0083)^-n=ln(0.6714)`

`:.-n*ln(1.0083)=ln(0.6714)`

`:.-n=ln(0.6714)/ln(1.0083)`

`:.-n=(-0.3983)/(0.0083)`

`:.-n=-48.0002`

`:.n=48.0002`

`:.n=49`

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

`507.25-166.6667=340.5833`

`20000-340.5833=19659.4167`

Month = 2
`19659.4167*0.008333=163.8285`

`507.25-163.8285=343.4215`

`19659.4167-343.4215=19315.9952`


Amortization table
MonthDatePrincipalInterestPaymentTotal Interest PaidTotal Remaining Balance
020000
1Mar-2024340.5833166.6667507.25166.666719659.4167
2Apr-2024343.4215163.8285507.25330.495219315.9952
3May-2024346.2834160.9666507.25491.461818969.7118
4Jun-2024349.1691158.0809507.25649.542718620.5427
5Jul-2024352.0788155.1712507.25804.713918268.4639
6Aug-2024355.0128152.2372507.25956.951117913.4511
7Sep-2024357.9712149.2788507.251106.229917555.4799
8Oct-2024360.9543146.2957507.251252.525617194.5256
9Nov-2024363.9623143.2877507.251395.813316830.5633
10Dec-2024366.9953140.2547507.251536.06816463.568
11Jan-2025370.0536137.1964507.251673.264416093.5144
12Feb-2025373.1374134.1126507.251807.37715720.377
13Mar-2025376.2469131.0031507.251938.380115344.1301
14Apr-2025379.3822127.8678507.252066.247914964.7479
15May-2025382.5438124.7062507.252190.954114582.2041
16Jun-2025385.7316121.5184507.252312.472514196.4725
17Jul-2025388.9461118.3039507.252430.776413807.5264
18Aug-2025392.1873115.0627507.252545.839113415.3391
19Sep-2025395.4555111.7945507.252657.633613019.8836
20Oct-2025398.751108.499507.252766.132612621.1326
21Nov-2025402.0739105.1761507.252871.308712219.0587
22Dec-2025405.4245101.8255507.252973.134211813.6342
23Jan-2026408.80398.447507.253071.581211404.8312
24Feb-2026412.209795.0403507.253166.621510992.6215
25Mar-2026415.644891.6052507.253258.226710576.9767
26Apr-2026419.108588.1415507.253346.368210157.8682
27May-2026422.601184.6489507.253431.01719735.2671
28Jun-2026426.122881.1272507.253512.14439309.1443
29Jul-2026429.673877.5762507.253589.72058879.4705
30Aug-2026433.254473.9956507.253663.71618446.2161
31Sep-2026436.864970.3851507.253734.10128009.3512
32Oct-2026440.505466.7446507.253800.84587568.8458
33Nov-2026444.176363.0737507.253863.91957124.6695
34Dec-2026447.877859.3722507.253923.29176676.7917
35Jan-2027451.610155.6399507.253978.93166225.1816
36Feb-2027455.373551.8765507.254030.80815769.8081
37Mar-2027459.168348.0817507.254078.88985310.6398
38Apr-2027462.994744.2553507.254123.14514847.6451
39May-2027466.85340.397507.254163.54214380.7921
40Jun-2027470.743436.5066507.254200.04873910.0487
41Jul-2027474.666332.5837507.254232.63243435.3824
42Aug-2027478.621828.6282507.254261.26062956.7606
43Sep-2027482.610324.6397507.254285.90032474.1503
44Oct-2027486.632120.6179507.254306.51821987.5182
45Nov-2027490.687316.5627507.254323.08091496.8309
46Dec-2027494.776412.4736507.254335.55451002.0545
47Jan-2028498.89958.3505507.254343.905503.155
48Feb-2028503.0574.193507.254348.0980.098
49Mar-20280.0980.00080.09884348.09880


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


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