Is it possible to figure out a complete amortization table with this information?

amortization
amy asked:


Someone has a 30-year home mortgage. In one year (not necessarily the first year) they paid 11,748.25 in interest only. In the following year, they paid $4,098.94 in principal and $11,549.53 in interest. Last year they paid $11,341 in interest. This year, what will the principal and interest payment be, and what is the interest rate?

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One Response to Is it possible to figure out a complete amortization table with this information?

  1. BobWang
    June 28, 2009 at 4:27 am

    I’m going to assume annual payments with no compounding to make the math easier.
    In principle, you can do the same with monthly payments, but it gets a lot messier.

    Number of years N = 30
    Payments per year P/YR = 1
    Yearly PMT = 4,098.94 + 11,549.53 = 15,648.47
    Future Value FV = 0

    Let B be the mortgage balance after $11,748.25 interest was paid for that year.
    Let I = interest rate
    The following year $11,549.53 in interest was paid, so

    Equation 1: B*I = 11,549.53

    The year of $11,341 in interest has to immediately follow, or I can’t see how to solve this thing, so

    Equation 2: (B-4,098.94)*I = 11,341 or B*I – 4098.94*I = 11,341

    Subtract equation 2 from equation 1 to get

    4098.94*I = 208.53
    I = .050874128433 = 5.0874128433%
    PV = 238,176.81 from any financial calculator, or Excel.

    Download the Excel amortization spreadsheet, and plug in numbers.
    Made up my own spreadsheet, ran Solver, but can’t get closer than $0.29 for the $11,748.25 interest payment.

    My solution is interest rate of 5.087%
    Interest payment of $11,121.86
    Principal payment of $4,526.61

    Interest5.09%
    Years30
    P/Yr1
    Loan amount238,165.85
    Rate (per period)5.09%
    PMT (per period)15,648.47

    NumberPMTInterestPrincipalBalance
    238,165.85
    115,648.4712116.483,531.99234,633.86
    215,648.4711936.7933,711.68230,922.18
    315,648.4711747.9653,900.51227,021.68
    415,648.4711549.534,098.94222,922.74
    515,648.47113414,307.47218,615.27
    615,648.4711121.8614,526.61214,088.66
    715,648.4710891.5744,756.90209,331.76
    815,648.4710649.5714,998.90204,332.86
    915,648.4710395.2565,253.21199,079.65
    1015,648.4710128.0045,520.47193,559.18
    1115,648.479847.15485,801.32187,757.87
    1215,648.479552.01796,096.45181,661.42
    1315,648.479241.86636,406.60175,254.81
    1415,648.478915.93596,732.53168,522.28
    1515,648.478573.42417,075.05161,447.23
    1615,648.478213.48737,434.98154,012.25
    1715,648.477835.2397,813.23146,199.02
    1815,648.477437.74778,210.72137,988.30
    1915,648.477020.03438,628.44129,359.86
    2015,648.476581.07029,067.40120,292.46
    2115,648.476119.77419,528.70110,763.77
    2215,648.475635.0110,013.46100,750.31
    2315,648.475125.58410,522.8990,227.42
    2415,648.474590.241311,058.2379,169.19
    2515,648.474027.663611,620.8167,548.38
    2615,648.473436.465212,212.0055,336.38
    2715,648.472815.190112,833.2842,503.10
    2815,648.472162.308213,486.1629,016.94
    2915,648.471476.211414,172.2614,844.68
    3015,648.47755.2101414,893.26-48.58

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