You Borrow money on a self liquidating installemnt loan (equal payments at the e

Question

You Borrow money on a self liquidating installemnt loan (equal payments at the end of each year, each payment is part princpr interest) Loan Interest Rate Life (years) Date of Loan 769,000 9.80% 52 anuary 1, 2016 Use the installment method-not straight line a) What is the annual payment? b) What is the total interest payments? c) After half the payments have been made, what percentage of the total interest has been paid (round to the nearest percentage point)? d) After half the payments have been made, what percentage of the total principal has been paid (round to the nearest percentage point)?

Explanation / Answer

Ans 1 Annual Payment=P*r(1+r)^n/(1+r)^n-1 769000*(.098(1.098)^52)/(1+.098)^52-1 769000*(.098*129.2176)/129.2176-1 Annual Payment 75949.77 Ans 2 Total Annual Payment 75949.77*52 years 3949387.85 Less: Principal Payment 769000 Total Interest Payment 3180387.85 Ans 3 Half the payment Interest amount (see working) 1912514.29 ) Ans 4 Half the payment Principal amount (see working) 62179.64 rounded off to two decimal Loan payment schedule Beginning value Principal P Interest on E Annual payment A Ending Value E= A-P 31-Dec-16 769000 587.77 75362.00 75949.77 768412.23 2 768412.23 645.37 75304.40 75949.77 767766.87 3 767766.87 708.61 75241.15 75949.77 767058.25 4 767058.25 778.06 75171.71 75949.77 766280.19 5 766280.19 854.31 75095.46 75949.77 765425.89 6 765425.89 938.03 75011.74 75949.77 764487.86 7 764487.86 1029.96 74919.81 75949.77 763457.90 8 763457.90 1130.89 74818.87 75949.77 762327.01 9 762327.01 1241.72 74708.05 75949.77 761085.29 10 761085.29 1363.41 74586.36 75949.77 759721.88 11 759721.88 1497.02 74452.74 75949.77 758224.86 12 758224.86 1643.73 74306.04 75949.77 756581.13 13 756581.13 1804.82 74144.95 75949.77 754776.31 14 754776.31 1981.69 73968.08 75949.77 752794.63 15 752794.63 2175.89 73773.87 75949.77 750618.73 16 750618.73 2389.13 73560.64 75949.77 748229.60 17 748229.60 2623.27 73326.50 75949.77 745606.34 18 745606.34 2880.35 73069.42 75949.77 742725.99 19 742725.99 3162.62 72787.15 75949.77 739563.37 20 739563.37 3472.56 72477.21 75949.77 736090.82 21 736090.82 3812.87 72136.90 75949.77 732277.95 22 732277.95 4186.53 71763.24 75949.77 728091.43 23 728091.43 4596.81 71352.96 75949.77 723494.62 24 723494.62 5047.29 70902.47 75949.77 718447.33 25 718447.33 5541.93 70407.84 75949.77 712905.40 26 712905.40 6085.04 69864.73 75949.77 706820.36 At the end of 26 year principal and interest paid 62179.64 1912514.29 27 706820.36 6681.37 69268.40 75949.77 700138.99 26 700138.99 7336.15 68613.62 75949.77 692802.84 28 692802.84 8055.09 67894.68 75949.77 684747.75 29 684747.75 8844.49 67105.28 75949.77 675903.27 30 675903.27 9711.25 66238.52 75949.77 666192.02 31 666192.02 10662.95 65286.82 75949.77 655529.07 32 655529.07 11707.92 64241.85 75949.77 643821.16 33 643821.16 12855.29 63094.47 75949.77 630965.86 34 630965.86 14115.11 61834.65 75949.77 616850.75 35 616850.75 15498.39 60451.37 75949.77 601352.36 36 601352.36 17017.24 58932.53 75949.77 584335.12 37 584335.12 18684.92 57264.84 75949.77 565650.20 38 565650.20 20516.05 55433.72 75949.77 545134.15 39 545134.15 22526.62 53423.15 75949.77 522607.53 40 522607.53 24734.23 51215.54 75949.77 497873.31 41 497873.31 27158.18 48791.58 75949.77 470715.12 42 470715.12 29819.68 46130.08 75949.77 440895.44 43 440895.44 32742.01 43207.75 75949.77 408153.43 44 408153.43 35950.73 39999.04 75949.77 372202.70 45 372202.70 39473.90 36475.86 75949.77 332728.79 46 332728.79 43342.34 32607.42 75949.77 289386.45 47 289386.45 47589.89 28359.87 75949.77 241796.55 48 241796.55 52253.70 23696.06 75949.77 189542.85 49 189542.85 57374.57 18575.20 75949.77 132168.28 50 132168.28 62997.27 12952.49 75949.77 69171.01 52 69171.01 69171.01 6778.76 75949.77 0.00 Total $769000.00 3180387.85 3949387.85

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