FM for Actuaries

168 CHAPTER 5
Therefore, the total monthly installment for the first year is
100,000 × 0.035
4,166.67 +
12
while that for the second year is
100,000 × 0.040
4,166.67 +
12
We solve for r ∗ from the equation
=$4,458.34
=$4,500.00.
4,458.34 a 12⌉ r ∗ +4,500.00 a 12⌉ r ∗ (1 + r ∗ ) −12 = 100,000
to obtain r ∗ =0.005856, so that the ENR in monthly rest is 12 × 0.005856 =
7.03%. The effective rate of interest of Option C is
(1.005856) 12 − 1=7.26%.
Hence, Option A has the lowest effective rate of interest, and Option B has the
highest effective rate of interest.
5.7 Borrowing Costs and Reference Rates
Apart from the differences in the ways interest is calculated, loans may vary in
the manner they charge other related fees. These may include administrative fees,
application fees, monthly fees and so on. To the effect that such fees may form a
significant portion of the costs in serving the loan, a loan that apparently charges a
lower rate of interest in nominal terms prior to such costs may turn out to be more
costly when such costs are properly accounted for. To help consumers choose a loan
in a well informed manner, regulators impose some guidelines that lenders have to
follow. Generally speaking, these regulations require the lenders to present their
loan offers in a representative or reference rate of interest that takes proper account
of any possible hidden costs and differences in computing the installments. The terminology
used by various regulatory bodies, however, does not always agree with
each other, or with the terms defined in the academic literature. These representative
rates or reference rates may be called by different names in different countries.
Furthermore, fine details are usually not available as to how the rates should be
computed. An accurate summary of the methodology used in different countries is
a difficult task.