Copyright © 2008, The McGraw-Hill Companies, Inc.
In the first month, the $2,000 premium is paid, which leaves $1,940.00 after the 3% load
is taken off. The mortality charge is calculated as follows. The death benefit is $100,000.
However, since the insurance company is holding an account value of $1,940 on the policy,
the insurance needs to provide only $100,000 $1,940 $98,060. (This amount is called
the net amount at risk.) So the term cost of insurance applies only to that amount of a
benefit; therefore it will cost (98.060)($0.043) $4.22. No interest is earned at the start
of the first month since the money has just been deposited. So the balance of the account
value is $1,940 $4.22 $2.50 $1,933.28. In the second month, the same process
is repeated, except that one month’s worth of interest will be paid on the $1,933.28 that
was on deposit for the month. At the end of the second month, then, the account value is
$1,933.28 $4.22 $2.50 $9.67 $1,936.23.
Whole life policies can be thought of as working in much the same way; the difference
is that with a whole life policy none of this is apparent to the policyholder. With a whole
life policy, the insurer sets a fixed premium, which has been determined in advance to
be adequate to carry the policy through the insured’s lifetime, with interest credited at an
assumed rate and the mortality costs charged at an assumed rate. With universal life, all of
this is transparent to the policyholder; the policy’s annual statement will show the interest
paid and fees charged directly. Universal life also offers the advantage that, while a set
premium may be scheduled for the policy, the policyholder may choose to pay more or less
than the scheduled premium.Example 13.3.5 Calculate the account value at the end of the third month for the
universal life insurance policy shown above. (Assume that no additional premiums are
paid.)In the third month, the net amount at risk is $100,000 $1,936.19 $98,063.81. So the
term cost is (98.06381)(0.043) $4.22. We also deduct the $2.50 monthly fee. Interest will
be earned equal to ($1,936.23)(0.06)(1/12) $9.68. Putting this all together, the account
value will be $1,936.23 $4.22 $2.50 $9.68 $1,939.19.MonthPremium
(Less Load)Mortality
Charge Fees Interest End Balance
1 $1,940.00 $4.22 $2.50 $0.00 $1,933.28
2 $0.00 $4.22 $2.50 $9.67 $1,936.23
3 $0.00 $4.22 $2.50 $9.68 $1,939.19A spreadsheet could be set up similar to the ones used in Chapter 5 to carry this out to
future months.
Notice that, since the monthly interest is higher than the cost of insurance, the policy’s
value is growing from month to month. This may, but does not need to, happen. If instead
you had deposited $500 in premium, the interest earnings would be less than the insur-
ance cost, and so the policy value would decline from month to month. However, a $500
premium would still be adequate to cover the insurance costs in the near term. One of the
advantages of universal life is that it allows a great degree of flexibility in how premiums
are paid. A policyholder who wants to pay a large premium up front, but then not pay much
thereafter, can. A policyholder who wants to make smaller but more frequent payments
can as well. Unlike whole life insurance, though, the policyholder can choose to vary the
premium amounts and timing to suit his needs.
To reflect the fact that the insurer undertakes large expenses of commissions, underwrit-
ing, and policy issue expenses up front, universal life policies usually carry a surrender
charge. If the policy is surrendered, the policyholder receives the policy’s account value
less the surrender charge. The account value less the surrender charge represents the cash
value of the policy at any given point in time. Surrender charges are usually huge in the
early years of the policy, declining to zero over a period of many years. A universal life
policy remains in good standing as long as the account value is larger than the surrender
charge. In the first few years of the policy, though, the account value is unlikely to be larger13.3 Life Insurance 555