Question
Suppose you buy a house for $640,000 and you have $90,000 in savings which you use as a down payment. The rest you finance with a 5-year mortgage with monthly payments and a quoted interest rate of 3.2% APR. In Canada, mortgage rates are quoted with semi-annual compounding, so this rate is an APR with semi-annual compounding and monthly payments.
(c) How much do you still owe after 3 years (i.e. immediately after you have paid the 36th payment)
(d) What is the amortization amount on the 37th mortgage payment?
Explanation / Answer
Amortization Schedule
We have to convert APR with semi-annual compounding to APR with monthly compounding
=12*(((1+3.2%/2)^2)^(1/12)-1)=3.1789%
Monthly payments=PMT(3.1789%/12,12*5,640000-90000)=9926.57
AMount owed after 36th payment=FV(3.1789%/12,36,-9926.57,640000-90000)=230526.46
In 37th payment
Payment=9926.57
Interest=230526.46*3.1789%/12=610.6842
Principal=9926.57-610.6842=9315.882
Month EMI Principal Interest Principal Outstanding 1 9926.565773 8469.57 1456.996 541530.4301 2 9926.565773 8492.007 1434.559 533038.4235 3 9926.565773 8514.503 1412.063 524523.921 4 9926.565773 8537.058 1389.508 515986.8628 5 9926.565773 8559.674 1366.892 507427.1892 6 9926.565773 8582.349 1344.217 498844.8403 7 9926.565773 8605.084 1321.482 490239.7561 8 9926.565773 8627.88 1298.686 481611.8763 9 9926.565773 8650.736 1275.83 472961.1405 10 9926.565773 8673.652 1252.913 464287.4882 11 9926.565773 8696.63 1229.936 455590.8587 12 9926.565773 8719.668 1206.898 446871.1911 13 9926.565773 8742.767 1183.799 438128.4243 14 9926.565773 8765.927 1160.639 429362.4973 15 9926.565773 8789.149 1137.417 420573.3485 16 9926.565773 8812.432 1114.134 411760.9166 17 9926.565773 8835.777 1090.789 402925.1398 18 9926.565773 8859.184 1067.382 394065.9563 19 9926.565773 8882.652 1043.914 385183.3041 20 9926.565773 8906.183 1020.383 376277.121 21 9926.565773 8929.776 996.7894 367347.3447 22 9926.565773 8953.432 973.1337 358393.9126 23 9926.565773 8977.15 949.4153 349416.7622 24 9926.565773 9000.932 925.6341 340415.8305 25 9926.565773 9024.776 901.7899 331391.0547 26 9926.565773 9048.683 877.8825 322342.3714 27 9926.565773 9072.654 853.9118 313269.7174 28 9926.565773 9096.688 829.8776 304173.0292 29 9926.565773 9120.786 805.7797 295052.2432 30 9926.565773 9144.948 781.618 285907.2954 31 9926.565773 9169.174 757.3923 276738.1219 32 9926.565773 9193.463 733.1023 267544.6584 33 9926.565773 9217.818 708.7481 258326.8408 34 9926.565773 9242.236 684.3293 249084.6043 35 9926.565773 9266.72 659.8459 239817.8844 36 9926.565773 9291.268 635.2976 230526.6162 37 9926.565773 9315.882 610.6842 221210.7346 38 9926.565773 9340.56 586.0057 211870.1745 39 9926.565773 9365.304 561.2617 202504.8705 40 9926.565773 9390.113 536.4523 193114.757 41 9926.565773 9414.989 511.5771 183699.7683 42 9926.565773 9439.93 486.636 174259.8386 43 9926.565773 9464.937 461.6288 164794.9016 44 9926.565773 9490.01 436.5554 155304.8913 45 9926.565773 9515.15 411.4156 145789.7411 46 9926.565773 9540.357 386.2092 136249.3845 47 9926.565773 9565.63 360.936 126683.7547 48 9926.565773 9590.97 335.5958 117092.7847 49 9926.565773 9616.377 310.1885 107476.4075 50 9926.565773 9641.852 284.714 97834.5557 51 9926.565773 9667.394 259.1719 88167.16182 52 9926.565773 9693.004 233.5622 78474.15821 53 9926.565773 9718.681 207.8846 68755.47702 54 9926.565773 9744.427 182.139 59011.05023 55 9926.565773 9770.241 156.3252 49240.80965 56 9926.565773 9796.123 130.443 39444.68688 57 9926.565773 9822.074 104.4923 29622.61337 58 9926.565773 9848.093 78.47277 19774.52037 59 9926.565773 9874.181 52.38435 9900.33895 60 9926.565773 9900.339 26.22682 0
