A calculate the monthly installment for the first 2

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annually after which it will increase to 6% annually. a) Calculate the monthly installment for the first 2 years. Ordinary Annuity
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C=?; where PVA = 400 000; k=0.05/12: n=20*12=240 C=$2639.82 b) Calculate the loan balance owing, at the end of the 2 nd year. PVA=? Where k=0.05/12; n=240-24=216 PVA=$375 489.74 c) Calculate monthly installments after 2 years. C=?; where PVA = 375 489.74; k=0.06/12: n=216 C=$2846.82 d) Calculate the difference in monthly payment from a change in interest rate from 5% to 6%. Increase in installment is $2846.82-$2639.82 = $207 e) If the installment remained unchanged, how much longer would it take to pay back the loan? PVA =375489.74; c=$2639.82: k=0.06/12 using ordinary annuity formula: 375489.74 = 2639.82[(1-(1+0.06/12 ) -n )/ 0.06/12] 142.24 = [(1-(1.005 ) -n )/ 0.06/12] 0.7112 = 1-(1.005 ) -n ) 0.2888 = 1.005 -n ln 0.2888/ln 1.005 = -n -249.02 = -n 249.02 = n So additional months is: 249-216 = 33 months approx. 3. Construct an amortization schedule of a loan of $10,000 to be repaid over 10 years with a 10- ordinary annuity payment at effective rate of interest of 10% per year. Where PVA = 10000; k=0.10; n= 10 C= 1627.45 Year Installment Int. Pmt Prin. Pmt Outstanding balance 0 10000 1 1627.45 1000.00 627.45 9372.55 2 1627.45 937.26 690.20 8682.36 3 1627.45 868.24 759.21 7923.14 4 1627.45 792.31 835.14 7088.00 5 1627.45 708.80 918.65 6169.36 6 1627.45 616.94 1010.51 5158.84 7 1627.45 515.88 1111.57 4047.27
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8 1627.45 404.73 1222.72 2824.55 9 1627.45 282.46 1344.99 1479.56 10 1627.45 147.96 1479.49 0.06 Note: Interest is calculated on previous years balance at 10% Principal pmt = installment –interest Outstanding balance = previous years outstanding balance – current years principal payment 4. Construct a sinking fund schedule for the loan of $15,000 to be repaid over 5 years with a 10- ordinary annuity payment at effective rate of interest of 8% per year. Where FVA = 15000; k=0.08/2; n= 10 C= 1249.36 (sinking fund deposit)X Year Installment Int. Pmt Sinking Fund deposit Sinking Fund int. Sinking Fund bal. 0 1 1849.36 600 1249.36 0.00 1249.36 2 1849.36 600 1249.36 49.97 2548.69 3 1849.36 600 1249.36 101.95 3900.00 4 1849.36 600 1249.36 156.00 5305.36 5 1849.36 600 1249.36 212.21 6766.94 6 1849.36 600 1249.36 270.68 8286.97 7 1849.36 600 1249.36 331.48 9867.81 8 1849.36 600 1249.36 394.71 11511.89 9 1849.36 600 1249.36 460.48 13221.72 10 1849.36 600 1249.36 528.87 14999.95 Note: Interest = 15000 x 0.08/2 =600 for each period as loan balance is same for all Installment = interest + sinking fund deposit Sinking fund int. = previous years sinking fund balance x 0.08/2 Sinking fund bal = previous years sinking fund balance + fund int. for this yr + sinking fund deposit for this yr THE END
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