10. A 20-year, $200,000 loan at a nominal annual interest rate of 12% convertibl
ID: 2776037 • Letter: 1
Question
10. A 20-year, $200,000 loan at a nominal annual interest rate of 12% convertible monthly is
being paid off via the sinking fund method. The nominal annual interest rate earned on
the sinking fund is 9% convertible monthly. Level sinking fund deposits and loan
interest payments are each made at the end of each month. What is the net amount of
interest paid during the 48th month of the loan? (Net interest during a given month is the
amount of interest paid on the loan, minus the amount of interest earned on the sinking
fund, during that month.)
Explanation / Answer
formula for monthly EMI, A = P x r(r+1)^n/((r+1)^n-1) Where P = 200,000, r = 12%/1200 = 0.01 and n = 20year x 12 = 240 month. So A = 200,000 x 0.01(1.01)^240/(1.01^240-1) Or, A = 200,000 x 0.01 x 10.89255/(10.89255-1) Or A = 200,000 x 0.108926/9.89255 Or, A = 200,000 x 0.011011 =2202.17 So we have to pay monthly 2202.17. in order to pay 2202.17 we need to make a sinking fund account, so that it will earn monthly 2202.17 at a interest rate of 9% Therefore Sinking Fund = 2202.17/(9%/12) = $293,622.7 Loan Principle Ending Nonth Balance Interest Repayment Balance 1 200000 2000 202.17 199797.8 2 199798 1997.978 204.1917 199593.6 3 199594 1995.936 206.2336 199387.4 4 199387 1993.874 208.296 199179.1 5 199179 1991.791 210.3789 198968.7 6 198969 1989.687 212.4827 198756.2 7 198756 1987.562 214.6075 198541.6 8 198542 1985.416 216.7536 198324.9 9 198325 1983.249 218.9211 198106 10 198106 1981.06 221.1104 197884.9 11 197885 1978.849 223.3215 197661.5 12 197662 1976.615 225.5547 197436 13 197436 1974.36 227.8102 197208.2 14 197208 1972.082 230.0883 196978.1 15 196978 1969.781 232.3892 196745.7 16 196746 1967.457 234.7131 196511 17 196511 1965.11 237.0602 196273.9 18 196274 1962.739 239.4308 196034.5 19 196034 1960.345 241.8251 195792.7 20 195793 1957.927 244.2434 195548.4 21 195548 1955.484 246.6858 195301.7 22 195302 1953.017 249.1527 195052.6 23 195053 1950.526 251.6442 194800.9 24 194801 1948.009 254.1606 194546.8 25 194547 1945.468 256.7023 194290.1 26 194290 1942.901 259.2693 194030.8 27 194031 1940.308 261.862 193768.9 28 193769 1937.689 264.4806 193504.5 29 193504 1935.045 267.1254 193237.3 30 193237 1932.373 269.7966 192967.5 31 192968 1929.675 272.4946 192695 32 192695 1926.95 275.2196 192419.8 33 192420 1924.198 277.9718 192141.9 34 192142 1921.419 280.7515 191861.1 35 191861 1918.611 283.559 191577.5 36 191578 1915.775 286.3946 191291.1 37 191291 1912.911 289.2585 191001.9 38 191002 1910.019 292.1511 190709.7 39 190710 1907.097 295.0726 190414.7 40 190415 1904.147 298.0233 190116.6 41 190117 1901.166 301.0036 189815.6 42 189816 1898.156 304.0136 189511.6 43 189512 1895.116 307.0538 189204.6 44 189205 1892.046 310.1243 188894.4 45 188894 1888.944 313.2255 188581.2 46 188581 1885.812 316.3578 188264.9 47 188265 1882.649 319.5214 187945.3 48 187945 1879.453 322.7166 187622.6 Total 93326.79 Total Interest payment = $ 93,326.80
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