FAQ 833: PPA/ARP Shortfall Payment Calculation using Segment Rates

Problem: How are the ARP21 15-year and PPA 7-year amortization payments for the funding shortfall calculated?

Solution: For the ARP21 15-Year shortfall amortization method, review the Example 1 below. For the PPA 7-year shortfall amortization method, review the Example 2 below. Both examples assume there are no prior amortization payments to consider. EXAMPLE 1 - ARP21 15-year amortization method The ARP21 funding shortfall amortization payment is calculated using the first two PPA Minimum tiered rates. EX: Funding rates are 4.75%, 5.00%, 5.74% Funding Shortfall = 123,226 Funding factor calculation: 1/(1.0475)^0 = 1.000000 1/(1.0475)^1 = 0.954654 1/(1.0475)^2 = 0.911364 1/(1.0475)^3 = 0.870037 1/(1.0475)^4 = 0.830585 1/(1.050)^5 = 0.783526 1/(1.050)^6 = 0.746215 1/(1.050)^7 = 0.710681 1/(1.050)^8 = 0.676839 1/(1.050)^9 = 0.644609 1/(1.050)^10 = 0.613913 1/(1.050)^11 = 0.584679 1/(1.050)^12 = 0.556837 1/(1.050)^13 = 0.530321 1/(1.050)^14 = 0.505068 Sum of 15 factors = 10.91933 123,226/10.91933 = 11,285.12 amortization payment for ARP21 15-year payment EXAMPLE 2 - PPA 7-year amortization method The PPA funding shortfall amortization payment is calculated using the first two PPA Minimum funding tiered rates. EX: Funding rates are 5%, 5.5%, 6% Funding Shortfall = 123,226 Funding factor calculation: 1/(1.05)^0 = 1.000000 1/(1.05)^1 = 0.952381 1/(1.05)^2 = 0.907029 1/(1.05)^3 = 0.863838 1/(1.05)^4 = 0.822702 1/(1.055)^5 = 0.765134 1/(1.055)^6 = 0.725246 Sum of 7 factors = 6.036331 123,226/6.036331 = 20,414.06 amortization payment for PPA 7-year payment