1. (1) Internal index. Example 1: Example 2:

   Example 1:

   Five-year guaranteed interest rate contract.

   Assume a contract issued three years ago with a five-year guaranteed interest rate of 12%. Currently, two-year single premium contracts are issued with a two-year guaranteed interest rate of 10%.

   The current cash surrender benefit is determined to be:

2. (i) CSB₃ = (1 − W₃) 0^A3 × ^1.122/_1.102

   Alternatively:

3. (ii) CSB₃ = (1 − W ₃)(0^A3)[1 − (.10 − .12) × 2]

   1. (2) External index. Example 3:

      Example 3:

      Five-year guaranteed interest rate contract.

      Assume a contract issued two-years ago with a five-year guaranteed interest rate of 9%. At issue, the yield to maturity on five-year Treasury bills was 10%. Currently, three -year Treasury bills are yielding 12% to maturity.

      The current cash surrender benefit is determined to be:

   Example 2:

   Five-year guaranteed interest rate contract with cap.

   Assume a contract issued three years ago with a guaranteed interest rate of 12% in years 1-5, and a minimum interest guarantee of 5% in years 6-10. There is a 5% cap on market value adjustments. Currently, two-year guaranteed interest rates of 8% are being offered on similar contracts.

   The current cash surrender benefit is determined to be:

   CSB₃ = (1 − W₃)0^A3 × ^1.122/_1.082 cap of 5%

   = (1 − W₃) 0^A3 × 1.05

4. (i) CSB₂ = (1 − W₂)0^A2 × ^{1.10 3}/_1.123

   Alternatively:

5. (ii) CSB₂ = (1 − W ₂)(0^A2)[1 − (.12 − .10) × 3]

   1. (1) Internal index. Example 4: Example 5:

      Example 4:

      Five-year flexible premium guaranteed interest rate contract.

      Assume a contract issued three years ago, and the guaranteed interest rates to maturity (five years from issue) associated with deposits made during the first three contract years are as follows:

      Time of deposit	Guaranteed interest rate to maturity
      0	10%
      1	9%
      2	9%

      Currently, two-year flexible premium contracts are issued with a guaranteed interest rate to maturity of 8½% on first-year deposits.

      The current cash surrender benefit is determined to be:

   (b) Flexible premium contracts.

6. (i) CSB₃ = (1 − W₃)(0^A3 ×^1.102/_1.0852 + 1^A3 × ^1.092/_1.0852 + 2^A3 × ^1.092)/_1.0852

   Alternatively:

7. (ii) Let i_avg = ^{0A3 × .10 + 1A3 × .09 + 2A3 × .09}/_{0A3 +1A3 + 2A3}

   Then:

   CSB₃ = [(1 − W ₃) × ((0^A3 + 1^A3 + 2^A3) × (1 + i_avg)²)]/(1.085)²

   Example 5:

   Five-year flexible premium, flexible maturity guaranteed interest rate contract.

   Assume a contract issued three years ago, and the guaranteed interest rates to maturity (five years from deposit) associated with deposits made during the first three contract years are as follows:

   Time of deposit	Guaranteed interest rate to maturity
   0	10%
   1	10%
   2	11%

   Currently, the following guaranteed interest rates are offered on deposits to new issues of similar contracts:

   Years to maturity	Guaranteed interest rate to maturity
   2	8%
   3	9%
   4	10%

   The current cash surrender benefit is determined to be:

8. (i) CSB₃ = (1 − W₃)(0^A3 ×^1.102/_1.082 + 1^A3 × ^1.103/_1.093 + 2^A3 × ^1.114)/_1.104

9. (ii) CSB₃ = (1 − W ₃)[(0^A3)[1 − (.08 − .10) × 2]

   + (1^A3)[1 − (.09 − .10) × 3]

   + (2^A3)[1 − (.10 − .11) × 4]]

   Alternatively:

   Let n_avg = ^{(0A3 × 2) + (1A3 × 3) + (2A3 × 4)}/_{(0A3 + 1A3 + 2A3}

   Assume n_avg = 3, Then:

10. (iii) CSB₃ = (1 − W ₃)(0^A3 × 1.10³ + 1^A3 × 1.10 ³ + 2^A3 × 1.11³)/1.093

    1. (2) External index. Example 6: Example 7:

       Example 6:

       Five-year flexible premium guaranteed interest rate contract.

       Assume a contract issued three years ago with a five-year guaranteed interest rate of 9%. The yield to maturity on Treasury bills during this period was as follows:

       Time	Years to maturity	T–bill yield to maturity
       0	5	10%
       1	4	9%
       2	3	9%

       Currently, two-year Treasury bills are yielding 8½% to maturity.

       The current cash surrender benefit is determined to be:

       CSB₃ = (1 − W₃)(0^A3 × ^1.102/_1.0852+ 1^A3 × ^1.092/_1.0852+ 2^A3 ×^1.092)/_{1.085 2}

       Example 7:

       Five-year flexible premium, flexible maturity guaranteed interest rate contract.

       Assume the same facts as in example 6, and further assume that the following market values of $1,000, semiannual coupon Treasury bills are known:

       Time	Years to maturity	Annual coupon rate	Market value
       0	5	10%	$1,000
       1	5	10%	$1,000
       2	5	11%	$1,000
       3	2	10%	$1,100
       3	3	10%	$1,100
       3	4	11%	$1,200

       The current cash surrender benefit is determined to be:

       CSB₃ = (1 − W₃)(0^A3 × ¹¹⁰⁰/₁₀₀₀ + 1^A3 × ¹¹⁰⁰/₁₀₀₀ + 2^A3 × ¹²⁰⁰⁾/₁₀₀₀

This section contains examples of the application of market-value adjustment formulae that meet the requirements of this regulation.

MARKET VALUE ADJUSTMENT EXAMPLES

Variables

x^A_t = Actual Accumulation Amount at time t derived from contribution made at time x

W_t = Withdrawal Charge Factor at time t

CSB_t = Cash Surrender Benefit at time t

(a) Single premium contracts.