Actuarial Notes

ACTUARIAL NOTES UPSecu25 TERM LIFE INSURANCE AND DEFERRED ANNUITY Peso, Non-Participating

PRODUCT DESCRIPTION UPSecu25 has the following features: 1. The death benefit equals to 100% of the policy amount will be given to the beneficiaries when the insured dies before reaching age 25. 2. Upon reaching age 18, the insured will receive 12% of the policy amount at the beginning of each year until age 25. 3. Premium Paying Period (PPP) is either 5-pay or 10-pay subject to a maximum age eligibility of the insured wherein payments can be made annually, semi-annually, quarterly or monthly through auto debit, cash, bank payments or agents. 4. Product is designed for child with maximum age of 10 for PPP of 10 years and maximum age of 15 for PPP of 5 years. 5. Age is calculated as of the insured’s last birthday.

ASSUMPTIONS 1. Mortality Rates a. Reserve Mortality Rates are based on 1973-78 Philippine Intercompany Table. This table is the same for both male and female and thus, age setback was done from age 18 wherein 𝑓 𝑞𝑥𝑚 = 𝑞𝑥+3 . b. Pricing Mortality Rates are based on 1 over 1.25 of 1973-78 Philippine Intercompany Table. 2. Interest Rates a. Interest rates used for pricing are based on Philippine Treasury Reference Rates - PM (PDST-R2). 25-year tenor has been chosen as the product is up to 25 years and the average of the rates from September 8 to September 30 is 4.71% b.

Interest rates used for reserve has been adjusted to a lower percentage which is 3.83%

3. Inflation Inflation rate is based on the maximum percentage which is 2.50% in the Summary Inflation Report Consumer Price Index for the year 2015 from Philippine Statistics Authority. 4. Commissions Policy Year 1 2 3 4 5 6 7 8 9 10

Payment Period 5-pay 10-pay 10% 15% 5% 10% 5% 10% 3% 5% 3% 5% 3% 3% 3% 3% 3%

5. Lapse and Surrender Rate Policy Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 – 25

Payment Period 5-pay 10-pay 15% 20% 10% 15% 10% 15% 5% 10% 5% 10% 3% 5% 3% 5% 3% 5% 3% 5% 3% 5% 2% 3% 2% 3% 2% 3% 2% 3% 2% 3% 1% 2% 1% 2% 1% 2% 1% 2% 1% 2% 1% 1%

6. Expenses a. Per Policy Expenses Expense Acquisition Maintenance (Premium Paying Period) Maintenance (Paid Up Period) Per Death Per Surrender Per Maturity

Amount, in PHP 1,000.00 500.00 100.00 1,000.00 750.00 250.00

b. Per 1000 of Policy Amount Expense Acquisition Maintenance Per Death Per Maturity

Per 1000 1.00 0.50 1.00 1.00

c. Percentage of Premium Expenses Expense Acquisition Maintenance (Premium Paying Period) Maintenance (Paid Up Period) Premium Taxes Local Government Tax

% of Premium 5.00% 2.00% 0.00% 2.00% 0.50%

FORMULATIONS 1. Term Life Insurance The death benefit payable at the moment of death for this term life insurance given age of insured, 𝑥, is calculated as 𝐷𝐵 where 𝛿 = ln(1 + 𝑖).

1 ⋅ 𝐴𝑥:25−𝑥|

𝑖 = 𝐷𝐵 ⋅ 𝛿

25−𝑥−1

∑ 𝑣 𝑘+1 𝑘 𝑝𝑥 𝑞𝑥+𝑘 𝑘=0

2. Endowment Benefit If the insured survives at age 18, insured will receive endowment benefit of 12% of the policy amount payable at the beginning of each year until age 25 given that insured is alive. The annuity is calculated as

18−𝑥| 𝑎̈ 𝑥:7|

={

0

,

𝑥 < 18

∑ 𝑣 𝑘 𝑘 𝑝𝑥

,

18 ≤ 𝑥 < 25

24−𝑥

𝑘=18−𝑥

3. Premium The Net Single Premium is computed as 1

𝑁𝑆𝑃 = 𝐷𝐵 (𝐴𝑥:25−𝑥| + 0.12 18−𝑥| 𝑎̈ 𝑥:7| ) . The Net Level Benefit Premium is equivalent to 𝑁𝐿𝐵𝑃 = where ℎ is the payment term.

𝑁𝑆𝑃 𝑎̈ 𝑥:ℎ|

4. Terminal Reserve

Prospective approach is used to compute for the terminal reserve. The terminal reserve is 𝑡𝑉

= 𝐷𝐵[ 𝑡 𝑉 (𝑡𝑒𝑟𝑚) + 0.12 𝑡 𝑉 (𝑒𝑛𝑑𝑜𝑤𝑚𝑒𝑛𝑡) ] − 𝑁𝐿𝐵𝑃 𝑡 𝑉 (𝑎𝑛𝑛𝑢𝑖𝑡𝑦)

where 1

(𝑡𝑒𝑟𝑚) = {𝐴𝑥+𝑡:25−𝑥−𝑡| 𝑡𝑉 0

𝑡𝑉

(𝑒𝑛𝑑𝑜𝑤𝑚𝑒𝑛𝑡)

𝑡𝑉

={

(𝑎𝑛𝑛𝑢𝑖𝑡𝑦)

𝑡 < 25 − 𝑥 𝑡 ≥ 25 − 𝑥

18−𝑥−𝑡| 𝑎̈ 𝑥+𝑡:7|

𝑡 < 18 − 𝑥

𝑎̈ 𝑥+𝑡:25−𝑥−𝑡|

𝑡 ≥ 18 − 𝑥

𝑎̈ = { 𝑥+𝑡:ℎ−𝑡| 0

𝑡