Answer:
$8,949.22
Explanation:
PV = annual payment x PV annuity factor
PV annuity factor = 14,133 / 1,000 = 14.133
PV annuity factor = [1 - 1/(1 + 0.063)ⁿ
] / 0.063
14.133 x 0.063 = 1 - 1/(1 + 0.063)ⁿ
0.890379 = 1 - 1/(1 + 0.063)ⁿ
1/(1 + 0.063)ⁿ = 0.109621
1 / 0.109621 = 1.063ⁿ
9.12234 = 1.063ⁿ
n = log 9.12234 / log 1.063 = 0.96010624 / 0.0265333 = 36
the present value of the first 36/4 = 9 payments = $1,000 x 6.71376 (PV annuity factor, 9 periods, 6.3%) = $6,713.76
the present value of the third set of 9 payments = $6,713.76 / (1 + 6.3%)¹⁸ = $2,235.46
present value of the first and third sets = $8,949.22
