When calendar year interest rates (a.k.a. select and ultimate interest rates) are used, unfunded liability bases are amortized by reflecting the duration and level of the full set of interest rates. That is, level annual installments are determined using the year-by-year interest rates.

For more information about this methodology, see the Society of Actuaries’ Transactions, volume XXXVII, "Select and Ultimate Financial Assumptions in Pension Plan Valuations: An Analysis of the Issues", pages 351-392.

EXAMPLE

Suppose the interest assumption is 10% the first year, 9% the second, and so forth, with the rate of 5% used after year 5. A liability of $100,000 is to be amortized over 30 years. The amortization payment is equal to $100,000 divided by the following sum:

The details of the amortization schedule are as follows:

year	B.O.Y. balance	B.O.Y. payment	Interest rate
1	100,000.00	6,986.60	10%
2	102,314.74	6,986.60	9%
3	103,907.68	6,986.60	8%
4	104,674.77	6,986.60	7%
5	104,526.35	6,986.60	6%
6	103,392.14	6,986.60	5%
7	101,225.82	6,986.60	5%
8	98,951.18	6,986.60	5%
9	96,562.81	6,986.60	5%
10	94,055.03	6,986.60	5%
11	91,421.85	6,986.60	5%
12	88,657.02	6,986.60	5%
13	85,753.95	6,986.60	5%
14	82,705.72	6,986.60	5%
15	79,505.08	6,986.60	5%
16	76,144.40	6,986.60	5%
17	72,615.70	6,986.60	5%
18	68,910.56	6,986.60	5%
19	65,020.16	6,986.60	5%
20	60,935.24	6,986.60	5%
21	56,646.08	6,986.60	5%
22	52,142.45	6,986.60	5%
23	47,413.65	6,986.60	5%
24	42,448.41	6,986.60	5%
25	37,234.90	6,986.60	5%
26	31,760.72	6,986.60	5%
27	26,012.83	6,986.60	5%
28	19,977.55	6,986.60	5%
29	13,640.50	6,986.60	5%
30	6,986.60	6,986.60	5%
31	0.00

 

Note that the resulting annual payment is less than interest during the first few years. Hence, the outstanding balance increases, even though the minimum payment has been made.