# Term Life Insurance (2): How much does it cost to insure my life?

If I had my way, I would write the word “insure” upon the door of every cottage and upon the blotting book of every public man, because I am convinced, for sacrifices so small, families and estates can be protected against catastrophes which would otherwise smash them up forever.

It is the duty to arrest the ghastly waste, not merely of human happiness, but national health and strength, which follows when, through the death of the breadwinner, the frail boat in which the family are embarked, founders and the women and children and the estates are left to struggle in the dark waters of a friendless world.Sir Winston Churchill

While Churchill is best remembered as the British Prime Minister who led the fight against Nazi Germany in World War II, he is less well known as the key figure who helped set up unemployment insurance and health insurance (through the National Health Service) in the United Kingdom, “bringing the magic of averages to the rescue of the millions”.

That, in a nutshell, is how term life insurance works. But how much does it cost? Suppose from experience we know that the chance of dying from any cause is 0.1% for a 40 year-old man. In theory, if every 40 year-old man paid $500 into an insurance fund, his family will receive $500,000 in the unfortunate instance him dying in that particular year.

This is not so far-fetched in practice. From the Singapore Life Tables, we can work out the mortality rate for every single age, and also the cumulative mortality over a period. We show this in the chart below:

###### Annual and Cumulative mortality rates for men in Singapore aged 25 to 65

*Source:* *Singapore Life Tables 2017/18*

We can see that the annual mortality rates for men are below 1% a year until the age of 65. Cumulatively however, there is a 1% chance of not surviving past the age of 42; a 2% chance of not surviving past the age of 50; a 5% chance of not surviving past the age of 57; and a 10% chance of not surviving until retirement age at 65. Based on this, we can work out the insurance premiums for insuring against death at any age. For example, if the chance of dying at the age of 62 is 1%, the premium for insuring that one year is $5,000 (divide the $500,000 coverage by 1%). This is what we show below:

###### Theoretical insurance premiums for each age group for coverage of $500,000

This is a chart of theoretical premiums to protect against the risk of death for 1 year only. As expected, it rises sharply once men get past the age of 45-50. In fact, the shape and level of the theoretical premiums mirrors some of the premiums which are payable on an annual renewable basis, like some group insurance policies. How does this work compare against the flat premiums which many insurance companies charge instead? Recall the cumulative chance of death for men between the age of 25 to 65 is roughly 10%. Does this mean that it costs $50,000 to insure against death over this 40 year period, or $1,250 per year? (i.e. $500,000 divided by 10%)

The answer is of course no! There is the time value of money to take into consideration, since we pay the annual premiums early on, and the possible claims are likely to be much later. On the other hand, there is also the chance that the claim will be put in early and there will be no further premiums to collect. Based on the mortality statistics for men, in theory, the annual level premium chargeable for $500,000 of coverage between age 25 to 65 is $919 per year. Which seems pretty high. So how much does it really cost to insure ourselves?

#### Cost of term life insurance in Singapore for men

To answer that question, we visit comparefirst.sg, a comparison website which provides indicative quotes for insurance products for many commercial insurers in Singapore. To help assess the value each insurance policy quoted to the buyer, we used the following assumptions:

- The buyer is 25 years old, and looking to cover himself until age 65 (40 years) for $500,000
- A discount rate of 3%, reflecting his youth, and hence ability to defer present gratification till the future
- The estimates for the mortality rates from the
*Singapore Life Tables 2017/18*

There is a pretty wide range of premiums across the different insurers. We only select those policies which have level premiums and coverage, and as few additional riders as possible. These annual premiums range between $338 to $609, with an average of $470. This is far below the theoretical estimate of $919 above!

###### Cost of term life insurance for 40 years to age 65 for men – Annual premiums and expected present value

*Source: CompareFIRST.sg*

We also compute the the expected present value of these polices (red line). Suppose the chance of surviving the five years until age 30 from age 25 is * y*%. Also suppose that the chance of dying at age 30 is

*%. So there is a*

**x***% chance of paying the annual premium that year, and a*

**y***% chance of collecting the $500,000 insured amount that year as well. We discount all these probability-weighted premium payments and insurance payouts back to age 25, and sum them all up. This gives us the expected present value. This is also the approach we use when computing the value of an annuity like CPF Life previously.*

**xy**This confirms the intuition that term life insurance is quite cheap in Singapore relative to the chance of death. The expected present values range between $7,000 to more than $13,000! Of course, these are just ** expected** values. There is a high chance that the insured person doesn’t pass away over this 40 year period, and hence end up with nothing for 40 years of premiums paid. But it is still helpful to know that buying term life insurance is good value, especially when comparing it to its more expensive cousin, whole life insurance.

We can also see that the expected value of the term insurance policy is negatively correlated with the annual premium. This in turn, positively correlates with the distribution cost (although not perfectly). Which leads to the conclusion that for simple products like term life insurance, it is better to try to minimise the distribution costs and premiums payable as far as possible.

Now, we may not want to get the same level of coverage for the entire 40 year period. After all, we do expect to succeed in our careers and save quite a bit of money over time. These savings can offset the need for a high amount of coverage, especially as we approach retirement. Would it be even better to buy term life insurance, but where the coverage decreased over time? This would be like mortgage insurance where the sum assured falls over time with the principal of the home loan.

Again, we looked up the indicative quotes from CompareFIRST.sg, and did the same calculations as before. Fewer insurers offer this, and the premiums are all slightly lower than before (between $328 and $485). This shows us:

###### Cost of decreasing term life insurance for 40 years to age 65 for men – Annual premiums and expected present value

*Source: CompareFIRST.sg*

Wait, what’s happening here? Unlike the previous chart when we looked at a constant coverage term life policy, here, for decreasing term life policies, the expected present values are all negative! In fact, we had originally expected the picture to look like this even for the constant coverage term life policies, because the insurer will charge a little over and above the actuarially fair rate for insurance to cover their costs. But it is indeed surprising that constant coverage term life insurance is such good value.

So, what’s going on here? Decreasing term life insurance has a higher coverage at the start than at the end of the policy. The negative expected present value leads us to suspect that term life insurance is fairly priced when the insured person is young (e.g. 25 to 35 years old) but is underpriced when he is older. This would mean that term life insurance for the ages of 35 to 65 would have an even higher expected present value!

Looking at yet another set of indicative quotes, this time for a man buying term life insurance for $500,000 of coverage from the age of 35 to 65. And this is what we see:

###### Cost of term life insurance for 30 years to age 65 for men from the age of 35 – Annual premiums and expected present value

*Source: CompareFIRST.sg*

The annual premiums are now higher, between $480 to $876 a year, but you pay for only 30 years max. Interestingly, the expected present values are now all even higher than before, ranging from $9,000 to more than $16,000! Basically, the later in life you get life insurance coverage, the cheaper it is. This confirms that term life insurance is fair value for the youngsters, but a bargain for the older folks. This also matches with what we said earlier, that term insurance to 99 years of age is a bargain to use for a legacy.

#### Do these costs and bargains in term life insurance work for women too?

Having seen what a bargain term life insurance can be for men, the next question is whether this applies for the women as well. So let’s start off by looking at a 25 year old women buying term life insurance to cover herself for $500,000 for 40 years until retirement.

###### Cost of term life insurance for 40 years to age 65 for women – Annual premiums and expected present value

*Source: CompareFIRST.sg*

Since women tend to live longer than men, we expect the annual premium they pay to be lower. And it is, ranging from $257 to $400, which is much less than the actuarially fair theoretical premium of $530. But the expected present values are also much lower than for the men, ranging between $3,000 to more than $6,000. So, women are still getting a good deal on term life insurance, just not as good a deal as men.

Is term life insurance also better value for the women the older they are when they start? Let’s take a look at the corresponding chart for decreasing term life insurance for women:

###### Cost of decreasing term insurance for 40 years to age 65 for women – Annual premiums and expected present value

*Source: CompareFIRST.sg*

This looks like the chart for decreasing term life insurance for men, except that the negative present values are now even more negative. So for decreasing term life insurance, women get a poorer deal than men.

Finally, let’s look at the premiums and expected value of term life insurance for women, starting from age 35, to age 65:

###### Cost of term life insurance for 30 years to age 65 for women from the age of 35 – Annual premiums and expected present value

*Source: CompareFIRST.sg*

As expected, the annual premiums are now higher (between $433 to $684). However, the expected present values are about the same as before (between $2,000 to $7,000). Putting all these together, term life insurance is still a good deal for women, but the underpricing is much less than for men. In fact, it may actually be expensive relative to the incidence of death or terminal disease for the younger years (between ages 25 to 35).

#### Some thoughts on term life insurance

So what are we to make of all this? Initially, we had suspected that term life insurance may be expensive in Singapore. It would appear so from the preference for financial advisors to recommend whole life insurance, as there will be some residual value to offset the lack of value in pure life insurance. However, we are proven wrong again!

- Term life insurance for men in Singapore is pretty cheap relative to mortality. So, it is worthwhile to get some coverage at the minimum.
- Term life insurance is even better value when the coverage starts at a later age. Say, at the age of 35, when there are liabilities such as a family and mortgage to take care of. This aligns well with how we should be planning our financial lives.
- Decreasing term insurance, on the other hand, has negative expected value, so don’t expect to get a good deal on your mortgage insurance!
- These findings also apply for women, although to a much smaller degree. The relative pricing of life insurance for women seems more expensive than for men

This leaves us wondering why the anomaly in pricing exists for men in Singapore? Perhaps it is due to underwriting: it is harder for a 35 year old man to get life insurance coverage, than it is for a 25 year old. At the age of 35, more illnesses and conditions may have surfaced, rendering the man ineligible for insurance. But while there are 30-year olds who unfortunately have critical illnesses, the incidence seems quite low. Or perhaps the underwriting experience of the insurance companies show that Singaporeans are getting healthier, live longer, and have a lower chance of death.

Regardless of the reason, it is to everyone’s benefit that the cost of term life insurance remains low and affordable. This allows us to use the savings from term life insurance to invest for our future. Just don’t buy too much decreasing term life insurance though …

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