The perils of ignoring opportunity cost

"Compound interest is the most powerful force in the universe." - Albert Einstein (attr.)

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2 3 weeks ago, My Paper The Business Times had a story about OCBC Bank's Mortgage Protector schemes which are unique among mortgage insurance plans in refunding buyers all the premiums they have paid at the end of the 20 year period (if they have made no claims).

As My Paper The Business Times notes, "These policies play right into the Singaporean psyche, which just hates giving or paying for something, for nothing in return".

Fortunately for OCBC, they also play right into economic illiteracy where people discount opportunity cost (in this case, forgetting that money should grow over time).

While My Paper The Business Times observes that these plans cost more than three times as much as non-refund plans, this is not the main problem with this "form of 'forced' savings".

Original Table:

	Regular-premium mortgage insurance plan with no-refund feature	Mortgage Protector Advantage
Premium amount per year	$1,760	$5,847
Total premiums paid over 15 years	$26,400	$87,700
Amount received at the end of policy term if no claim is made throughout the term	$0 (there is no refund)	$87,700

Assumptions: 40 years old, male, non-smoker, sum assured $1 million, 20-year policy term, 5% interest rate

Using the same assumption of a 5% interest rate, let us calculate the real value of the payments one makes to OCBC. Besides the $5,847 annual payment, we must each year multiply the value of all the premiums paid in previous years by the prevailing interest rate of 5%.

5% Interest Rate
Year	Value of Premiums
1	$ 5,847
2	$ 11,986
3	$ 18,433
4	$ 25,201
5	$ 32,308
6	$ 39,771
7	$ 47,606
8	$ 55,834
9	$ 64,472
10	$ 73,543
11	$ 83,067
12	$ 93,067
13	$ 103,568
14	$ 114,593
15	$ 126,170
Refund	$ 87,700
Net 'Loss'	$ 38,470
Extra Expenditure over regular plan	$ 12,070

So we can see that at a 5% interest rate, you're actually paying $12,070 more than with a regular plan - even after a refund (which is by no means guaranteed, since you might need to file a claim for the policy).

From there it is a trivial exercise to calculate the interest rate at which one's 'losses' (in opportunity cost) are 0 - 3.653% (of course, a different interest rate would change the plan's numbers too, but for simplicity let's hold them constant and treat this as a simple exercise in opportunity cost).

3.653% Interest Rate
Year	Value of Premiums
1	$ 5,847
2	$ 11,908
3	$ 18,189
4	$ 24,701
5	$ 31,450
6	$ 38,446
7	$ 45,697
8	$ 53,213
9	$ 61,004
10	$ 69,079
11	$ 77,449
12	$ 86,125
13	$ 95,117
14	$ 104,439
15	$ 114,100
Refund	$ 87,700
Net 'Loss'	$ 26,400
Extra Expenditure over regular plan	$ 0

Again, all this assumes that there is no claim - if you make a claim you don't even get anything back. So this is assuredly a bad plan, unless you think you are a terrible investor who will definitely never make a claim.