Premium Income is the cash paid by policyholders to the insurance company. For traditional policies, Insurers normally will classify premium into two types:
1. Single Premium
2. Regular Premium
Single premium means that, the policyholder only pays 1 large premium at the beginning of the contract. Regular premium means the policyholder is regularly paying premium (say, monthly for 10 years) into the insurance contract.
For UL policies, "Top-Up Premium" may also exist, meaning the "extra premium" that the policyholder puts into the contract on top of the promised regular premium.
Premium can be paid in different frequency, namely:
1. Yearly
2. Half-yearly
3. Quarterly
4. Monthly
Insurers called this the "premium frequency" or "pay mode". Since monthly premium means that the policyholder can pay most of premiums later (compare to paying as a lump sum at the beginning of the year), insurers may loss the time value of money. Hence, some adjustment has to be made for different premium frequency to "load-up" the premium charges.
To adjust for this timing differences, insurers will multiply a "modal factor" to the annual premium. Modal factor is a multiplicative factor varies with premium frequency. A typical modal factor table is shown as below:
Assume the annual premium is 100. The calculation for other pay-mode is as below:
Half-yearly: 100 * 0.51 = 51
Quarterly: 100 * 0.26 = 26
Monthly: 100 * 0.0875 = 8.75
One can see that, the more frequent the pay-mode, the more expensive the policy is. Since:
Half-yearly: 51 * 2 = 102
Quarterly: 26 * 4 = 104
Monthly: 8.75 * 12 = 105
The calculation for premium income is simple, it is just the annual premium, multiplied by the modal factor, then multiplied by the number of policy inforce at start of period. (you won't expect someone died to pay premium right?) Beware of the cashflow timing, since premium is collected at the start of period, it is a beginning of period (BOP) cashflow.
\begin{equation}
\begin{split}
Premium\_Income\_PerPolicy _t & = Annual\_Premium × Modal\_Factor \\
Premium\_Income _t & = Premium\_Income\_PerPolicy _t × Number\_of\_Inforce\_Start _t
\end{split}
\end{equation}
Using abbreviation:
\begin{equation}
\begin{split}
PREM\_INC\_PP _t & = ANN\_PREM × MODAL\_FAC \\
PREM\_INC _t & = PREM\_INC\_PP _t × NOP\_IFSM _t
\end{split}
\end{equation}
We shall use the same double decrement model we have introduced in previous chapters. Assume premium payment period (PPP) is 5 years, and the annual premium is 100. The pay-mode is annually.
Year 1
PREM_INC_PP = 100 * 1 = 100
PREM_INC = 100 * 1 = 100
Year 2
PREM_INC_PP = 100 * 1 = 100
PREM_INC = 100 * 0.899835 = 89.98
...
Year 5
PREM_INC_PP = 100 * 1 = 100
PREM_INC = 100 * 0.828174 = 82.82
A demonstration spreadsheet showing the calculation above can be downloaded here:
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