List price of new car = $19,858 Value of old car = $4,384 Amount traded in with old car = 85% of $4,384 = 0.85 x $4,384 = $3,726.40 Amount owed after trade in = $19,858 - $3,726.40 = $16,131.60 Value of sales tax = 9.27% of $19,858 = 0.0927 x $19,858 = $1,840.84 Total amount owed after purchase of car = $16,131.60 + $1,840.84 + $988 + $77 = $19,037.44
Since she is liduidating the dept by a series of monthly payments, this amounts to an annuity liqidation with present value (PV) = $19,037.44; rate (r) = 9.5% = 0.095; n = four years.
The present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt) / (r/t); where P is the periodic payment, i.e. monthly payment; and t is the number of payments in one year. 19,037.44 = P(1 - (1 + 0.095/12)^-(4 x 12)) / (0.095 / 12) (0.095 x 19,037.44) / 12 = P(1 - (1 + 0.095/12)^-48) 150.7131 = P(1 - 0.6849) = 0.3151P P = 150.7131 / 0.3151 = $478.28
Thus, she is supposed to be making a monthly payment of $478.28. Since she pays $550 monthly, therefore, she pays $550 - $478.28 = $71.72 extra every month.
Since line t is a transversal line all angle which are perpendicular with 63 will equal to the same value (63) and also line m is a straight line where it’s total will be 180
So, 3x + 2x + 63 = 180 5x + 63 = 180 5x = 180 - 63 5x = 117 Divide by 5 throughout X = 23.4degrees
