Question

Kimiko signed a loan agreement requiring payments of $234.60 at the end of every month for six years at 7.2% compounded monthly.

1. (a) How much was the original loan balance?

2. (b) If Kimiko missed the first five payments, how much would she have to pay after six months to bring the payments up to date?

3. (c) How much would Kimiko have to pay after six months to pay off the loan (assuming she missed all the payments and there was no late payment penalty)?

4. (d) If the loan were paid off after six months, what would the total interest cost be?

5. (e) How much of the total interest cost is additional interest because of the missed payments

Answer 1

Facts	EMI =	$234.60
	Rate=	7.20%	compunded amonthly
	Monthly interest rate=	0.6%
	No of month	72 month
	placed in formula
1	EMI=	(P*R*(1+R)^N)/(1+R)^N-1
	Principal	EMI*((1+R)^n-1)/R*(1+R)^n
		13835
2	Miss First five installment
	As we see in yellow highlighted area if install ment not paid for First five then total debt amont will be 14255.6
	If installment paid on time then total debt amount after five installment will be 13067.9
	After 6 month he has to paid to get the apyment up to date = 14255.6-13067.9+ EMI
					1422.3
3	If he miss all payment then after 6 month to payoff loan he has to paid amount refre yellow portion
	Amount to be paid =	14340.59
4	if loan paid off after 6 month intt cost will be refer green portion
	Amount would be	505.59
5	The extra intt cost because of missed payment is
	Sum of intt if EMI paid on time=	484.31
	Sum of intt if EMI not paid on time=	505.59
	Extra intt cost	21.28
	Initial 13835 Month EMI Principal Intt O/S amount If EMI not paid INTT Amount 1 234.6 151.59 83.01 13683.41 83.01 13918.01 2 234.6 152.50 82.10 13530.91 83.51 14001.52 3 234.6 153.41 81.19 13377.50 84.01 14085.53 4 234.6 154.34 80.26 13223.16 84.51 14170.04 5 234.6 155.26 79.34 13067.90 85.02 14255.06 6 234.6 156.19 78.41 12911.71 85.53 14340.59 7 234.6 157.13 77.47 12754.58 total 505.59 8 234.6 158.07 76.53 12596.50 9 234.6 159.02 75.58 12437.48 10 234.6 159.98 74.62 12277.51 11 234.6 160.93 73.67 12116.57 12 234.6 161.90 72.70 11954.67 13 234.6 162.87 71.73 11791.80 14 234.6 163.85 70.75 11627.95 15 234.6 164.83 69.77 11463.12 16 234.6 165.82 68.78 11297.30 17 234.6 166.82 67.78 11130.48 18 234.6 167.82 66.78 10962.67 19 234.6 168.82 65.78 10793.84 20 234.6 169.84 64.76 10624.00 21 234.6 170.86 63.74 10453.15 22 234.6 171.88 62.72 10281.27 23 234.6 172.91 61.69 10108.35 24 234.6 173.95 60.65 9934.41 25 234.6 174.99 59.61 9759.41 26 234.6 176.04 58.56 9583.37 27 234.6 177.10 57.50 9406.27 28 234.6 178.16 56.44 9228.11 29 234.6 179.23 55.37 9048.87 30 234.6 180.31 54.29 8868.57 31 234.6 181.39 53.21 8687.18 32 234.6 182.48 52.12 8504.70 33 234.6 183.57 51.03 8321.13 34 234.6 184.67 49.93 8136.46 35 234.6 185.78 48.82 7950.68 36 234.6 186.90 47.70 7763.78 37 234.6 188.02 46.58 7575.76 38 234.6 189.15 45.45 7386.62 39 234.6 190.28 44.32 7196.34 40 234.6 191.42 43.18 7004.91 41 234.6 192.57 42.03 6812.34 42 234.6 193.73 40.87 6618.62 43 234.6 194.89 39.71 6423.73 44 234.6 196.06 38.54 6227.67 45 234.6 197.23 37.37 6030.44 46 234.6 198.42 36.18 5832.02 47 234.6 199.61 34.99 5632.41 48 234.6 200.81 33.79 5431.61 49 234.6 202.01 32.59 5229.60 50 234.6 203.22 31.38 5026.38 51 234.6 204.44 30.16 4821.93 52 234.6 205.67 28.93 4616.26 53 234.6 206.90 27.70 4409.36 54 234.6 208.14 26.46 4201.22 55 234.6 209.39 25.21 3991.83 56 234.6 210.65 23.95 3781.18 57 234.6 211.91 22.69 3569.26 58 234.6 213.18 21.42 3356.08 59 234.6 214.46 20.14 3141.62 60 234.6 215.75 18.85 2925.87 61 234.6 217.04 17.56 2708.82 62 234.6 218.35 16.25 2490.47 63 234.6 219.66 14.94 2270.82 64 234.6 220.98 13.62 2049.84 65 234.6 222.30 12.30 1827.54 66 234.6 223.63 10.97 1603.91 67 234.6 224.98 9.62 1378.93 68 234.6 226.33 8.27 1152.60 69 234.6 227.68 6.92 924.92 70 234.6 229.05 5.55 695.87 71 234.6 230.42 4.18 465.44 72 234.6 231.81 2.79 233.64