# selected answers for chapters 13, 5 (Miller et al., ninth edition)

p.797 - 18: 2370 ×(1 + (.1/4))^(5 × 4) = 3883.52; 3883-52 - 1513.52

Also: Using the table on page 824, if you have a 20 year mortgage for \$80,000 at 7%,
a) what is your monthly payment? 80 × 7.75299 = 620.2392
b) what is the total of all your payments? 20 × 12 × 620.2392 = 148857.41
c) how much interest will you pay in total? 148857.41 - 80000 = 68857.41
d) what fraction of your total payments is interest? 68857.41/148857.41 = .4626
e) what fraction of your first payment is interest? (80000 × .07/12)/620.24 = .7524

p.239 - Also: Find all solutions to 2 + x = 3 (mod 5) We want 2+x = 3, 8, 13, 18, etc., hence x = 1, 6, 11, 16, etc. (including -4, -9, etc.)
Find all solutions to 2x = 3 (mod 5) We want 2x = 3, 8, 13, 18, etc., hence x = 1.5, 4, 6.5, 9, etc. (including -1, -3.5, -6, etc.)
If September 1 is a Tuesday, what day of the week is October 1? 1+(4 × 7) = 29 so September 29 is a tuesday, two days later is a thursday. (or, the number of days in September is 2 (mod 7), hence October 1 is two days later than September 1)