How lenders exploit Truth-in-Lending's
Why stop at 365?
An APR divisor of 10,000 adds almost nothing
to the interest paid on a typical loan
Legally, a lender could observe the
number of hours (minutes or seconds) between
payment dates and base a loan's periodic rate
on hours (minutes or seconds) between dates.
The advantage of more frequent division of APR
(to pPR, the perPeriodRate) is that it permits
a lender to receive more interest on the same
nominal APR than the loan would yield
with fewer APR divisions.
Lenders maximize the division of APR
(Annual Percentage Rate) to the periodic rate
A large APR divisor means more interest income for
lenders, while preserving the same nominal APR
they quote to you.
This is legal
If a lender observes the number of days (e.g: in a
month), they can base a loan's periodic rate on days
(rather than months), and payments on days between
monthly payment dates.
365 is about the largest practical divisor. Any divisor
larger than 365 would be difficult to justify - no one
borrows by the hour. Since the return from large divisors is
small, no lender finds it worthwhile to antagonize
regulators and borrowers with a scheme to charge interest
by the hour. Though you can be sure, were the return
significant, lenders would would find a way to overcome
A lender-optimized 365-divisor days-between-dates loan
APR, nominal dec. 0.13 <- "13.000% Annually"
Term (mo) 48
Pmt, "monthly" [a] 268.84 <- from lender's table
First Period's interest 110.41 <- calculated
Last Pmt [b] 235.40 <- from lender's table
a] The monthly Pmt amount is arbitrary. It is designed to
over repay (on a straight amortization basis), then
close-out the loan with a smaller last payment.
Calculate perPeriodRate (pPR):
NOTE: This loan uses a daily pPR, perPeriod Rate.
pPR(daily)= APR/100/365= 13/100/365 = 0.000356
from the pPR, it follows:
APR = pPR*365*100 = (.000356*365*100) = 13
Yield, % = 100*((1+0.000356)^365-1) = 13.88020
This amortization table uses days-between-dates:
Pmt_# Date Day Pmt IntPd PrinPd PrinBal
Init 10/15/97 na na na 10000.00
1 11/15/97 31 268.84 110.41 158.43 9841.57
2 12/15/97 30 268.84 105.16 163.68 9677.89
3 1/15/98 31 268.84 106.85 161.99 9515.90
4 2/15/98 31 268.84 105.07 163.77 9352.13
[. . . table is truncated for online viewing]
46 8/15/2001 31 268.84 8.36 260.48 496.26
47 9/15/2001 31 268.84 5.48 263.36 232.90
48 10/15/2001 30 235.40 2.49 232.91 -0.01 [b]
b] The balance doesn't end in zero. It should. But it doesn't.
The spreadsheet accurately reproduces an amortization table
furnished by a lender for a real loan. Why make things up
when reality is more fun?
- Truth-in-Lending's APR
is a nominal rate. "Nominal" means "in name only." APR is the
calculation lenders could agree upon at the time
Truth-in-Lending was legislated.
APR is adjusted by time-geometric, division and
multiplication, and by time-exponential, powers and roots. True
rates are adjusted by time-exponential, powers and roots, only. APY (Federal
Reserve Reg. DD, Truth-in-Savings) is a true rate.
The difference between a nominal rate (APR on loans), and a
true rate (APY on savings) makes it possible (were there no
overhead) for lenders to borrow savings and lend them at the
same stated rate and make money. «back»