Answer:
the % of the present value that corresponds to the first 9 payments (N) = 47.57% of the annuity's present value.
the % of the present value that corresponds to the first 27 payments (3N) = 90.86% of the annuity's present value.
Explanation:
we must use the present value of an annuity formula:
PV = annual payment x annuity factor
14,113 = 1,000 x annuity factor
annuity factor = 14,113 / 1,000 = 14.133
we know that the interest rate is 6.3%, now using an annuity calculator we can determine that the total number of periods is 36. The exact factor is 14.11322, but we can round to 14.113
the first set would represent 36/4 = 9 years
the % of the present value that corresponds to the first 9 payments (N) = PV = 1,000 x 6.71376 (PV annuity factor, 6.3%, 9 periods) = 6,713.76. This corresponds to 6,713.76 / 14,113 = 47.57% of the annuity's present value.
the % of the present value that corresponds to the first 27 payments (3N) = PV = 1,000 x 12.82329 (PV annuity factor, 6.3%, 27 periods) = 12,823.29. This corresponds to 12,823.29 / 14,113 = 90.86% of the annuity's present value.
