The Cost of Fractional Premiums

Posted at on July 25, 2009

I renewed my apartment lease a few weeks ago. After September, my rent will go down — thanks, recession! — from $2,500 to $2,400. I asked my landlord what lump sum he would want if I paid six months of rent (August through January) in July. This is not a typical request from a tenant, so he took a few hours to think about it and came back with an offer of $14,000. That’s $600 or about 4.1% less than the total monthly rent of $14,600 (two months of $2,500 and four months of $2,400).

By accepting his offer, I’ll have to pay $11,500 in addition to the $2,500 rent that I would otherwise pay for August. What is the annualized rate of return (IRR) on my $11,500 investment?

  1. 4.1%
  2. 8.2%
  3. 17.4%
  4. 22.8%

The correct answer is D. The annualized IRR of an outflow of $11,500 followed at monthly intervals by an inflow of $2,500 and four inflows of $2,400 is 22.84%. Said another way, the present value of two monthly payments of $2,500 and four monthly payments of $2,400, discounted at an annualized 22.84%, is $14,000.

This high rate of return will not surprise anyone who is familiar with the cost of fractional premiums; that is, premiums that are paid semi-annually, quarterly or monthly rather than annually. Fractional premiums are also called modal premiums. When you buy a fixed-premium insurance policy — term insurance, traditional whole life, disability income insurance, long-term care insurance — you will probably face a financial decision that is similar to my rent decision. (Flexible-premium insurance policies, such as universal life and variable universal life, also have a choice of premium modes, but the financial decision is different.)

According to 20-year term quotes from Compulife, a $500,000 MetLife policy issued to a 40-year-old female preferred nonsmoker has an annual premium of $469.00, a semi-annual premium of $248.57, a quarterly premium of $126.63, and a monthly premium of $42.22. Here is the cost of each option, expressed in dollars and as an annualized IRR:

Modal premium Total premiums Annualized IRR
Annual $469.00 $469.00
Semi-annual 248.57 497.14 27.2%
Quarterly 126.63 506.52 23.3%
Monthly 42.22 506.64 18.7%

By paying annually rather than semi-annually, you save $28.14 and you earn a 27.2% annualized return on the $220.43 prepayment. By paying annually rather than quarterly, you save $37.52 and you earn a 23.3% return on the $342.37 prepayment. By paying annually rather than monthly, you save $37.64 and you earn an 18.7% return on the $426.78 prepayment.

Here are the costs for the monthly premium mode for a few other companies:

Annual premium Monthly premium IRR
Ohio National $395.00 $35.16 14.7%
AXA Equitable 415.00 38.07 21.6%
Ameritas 470.00 41.13 10.8%
TIAA-CREF 508.05 44.45 10.8%
Guardian 515.00 44.20 6.5%
Prudential 515.00 46.35 17.2%

The charges for fractional premiums compensate the insurance company for lost interest, higher administrative costs and higher lapses. A high charge does not necessarily mean a high profit for the company.

From the policyholder’s perspective, the charges are not tax deductible, although they do add to the cost basis and therefore reduce any taxable gain upon surrender.

Another consideration in choosing a premium mode is what happens if you die or discontinue the policy. Is there a refund of any unearned premium? That varies by company and type of policy.

Joseph M. Belth, a retired insurance professor and the editor and publisher of The Insurance Forum, has created a handy online calculator at Note, however, that this provides the annual percentage rate (APR), not the internal rate of return (IRR). The APR is a nominal rate that ignores compounding, so it is slightly less than the IRR.