Math 2580 Test Math 2580 Test #1 Answers
For each question, there are 3 answers because there are 3 versions of the test.
To find your version, look at question #1:
ver.1 has \$12000, ver.2 has \$14000 and ver.3 has \$15000.

marks: 1-7; 2(a)-6; 2(b)-4; 3-7; 4(a)-5; 4(b)-5; 5-7; 6-9

1. 12000(1-0.04)(1+((90-15)/365)r) = 12000; r = ((1/0.96)-1)(365/75) = 0.2027778 = 20.278%

14000(1-0.04)(1+((90-20)/365)r) = 14000; r = ((1/0.96)-1)(365/70) = 0.2172619 = 21.726%

15000(1-0.03)(1+((60-10)/365)r) = 15000; r = ((1/0.97)-1)(365/50) = 0.225773 = 22.577%

2. (a) bank pays 4000(1+((352-174)/365)(0.10))(1+((352-248)/365)(0.13))-1 = \$4045.23

(b) 4045.23(1+((349-248)/365)r) = 4000(1+((349-174)/365)(0.10)) = 4191.78 so the bank gets r = ((4191.78/4045.23)-1)(365/101) = 0.130923 = 13.0923%

(a) bank pays 5000(1+((349-179)/365)(0.08))(1+((349-255)/365)(0.12))-1 = \$5030.83

(b) 5030.83(1+((346-255)/365)r) = 5000(1+((346-179)/365)(0.08)) = 5183.01 so the bank gets r = ((5183.01/5030.83)-1)(365/91) = 0.121333 = 12.1333%

(a) bank pays 6000(1+((347-179)/365)(0.09))(1+((347-257)/365)(0.12))-1 = \$6068.97

(b) 6068.97(1+((344-257)/365)r) = 6000(1+((344-179)/365)(0.09)) = 6244.11 so the bank gets r = ((6244.11/6068.97)-1)(365/87) = 0.1210718 = 12.1072%

3. ej¥ = (1+0.084/4)4 = 1.0214 so j¥ = 4LN(1.021) = 0.0831301 = 8.313%

ej¥ = (1+0.094/2)2 = 1.0472 so j¥ = 2LN(1.047) = 0.09185786 = 9.1858%

e0.104 = (1+j12/12)12 so j12 = 12(e0.104/12-1) = 0.10445197 = 10.4452%

4. (a) MR: 2000(1+(11/12)(0.0925))-900(1+(8/12)(0.0925))-800(1+(4/12)(0.0925)) = \$389.44
(b) DBM: 3 mo: 2000(1+(3/12)(0.0925))-900 = \$1146.25;
7 mo: 1146.25(1+(4/12)(0.0925))-800 = \$381.59;
11 mo: 381.59(1+(4/12)(0.0925)) = \$393.36

(a) MR: 2000(1+(10/12)(0.0825))-800(1+(6/12)(0.0825))-900(1+(4/12)(0.0825)) = \$379.75
(b) DBM: 4 mo: 2000(1+(4/12)(0.0825))-800 = \$1255.00;
6 mo: 1255.00(1+(2/12)(0.0825))-900 = \$372.26;
10 mo: 372.26(1+(4/12)(0.0825)) = \$382.49

(a) MR: 3000(1+(10/12)(0.1025))-1200(1+(6/12)(0.1025))-1300(1+(3/12)(0.1025)) = \$661.44
(b) DBM: 4 mo: 3000(1+(4/12)(0.1025))-1200 = \$1902.50;
7 mo: 1902.50(1+(3/12)(0.1025))-300 = \$651.25;
10 mo: 651.25(1+(3/12)(0.1025)) = \$667.94

5. 50000(1+0.085/2)-20(1+(5/12)(0.085)) = \$22519.77
50000(1+0.095/2)-17(1+(1/12)(0.095)) = \$22896.87
50000(1+0.097/2)-13(1+(1/12)(0.097)) = \$27231.83

6. 8000-X(1+0.072/12)-7-X(1+0.072/12)-9-X(1+0.072/12)-11 = 0 so
X = 8000/((1+0.072/12)-7+(1+0.072/12)-9+(1+0.072/12)-11) = \$2814.04

9000-X(1+0.092/12)-6-X(1+0.092/12)-9-X(1+0.092/12)-10 = 0 so
X = 9000/((1+0.092/12)-6+(1+0.092/12)-9+(1+0.092/12)-10) = \$3196.87

7000-X(1+0.097/12)-6-X(1+0.097/12)-9-X(1+0.097/12)-11 = 0 so
X = 7000/((1+0.097/12)-6+(1+0.097/12)-9+(1+0.097/12)-11) = \$2501.61

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On 8 Nov 2000, 14:31.