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Quick Facts...
- The annual percentage rate provides a common basis to compare interest charges associated with the loan. The contractual rate is the interest rate actually stated on the loan contract.
- Lenders use the add-on method, the discount method and the remaining balance method to calculate interest charges. Agricultural lenders do not commonly use the first two methods.
- The annual percentage rate stated for loans also should reflect all loan service costs and stock purchase requirements.
Any time money is borrowed, interest is charged. How interest is
computed often is confusing, as is the manner in which the interest rate is
stated. The federal Truth in Lending Act of 1968 (and its successor, the Truth
in Lending Simplification and Reform Act of 1980) "was enacted in order to
assure a meaningful disclosure of credit terms and to protect the Consumer
against inaccurate and unfair credit billing and credit card practices. The
act imposes detailed reporting requirements on lenders. However, agricultural
transactions are fully excluded from its application." (Uchtmann, D.L., J. W.
Looney, N.G.P. Krausz, and H.W. Hannah, Agricultural Law: Principles and
Cases. New York: McGraw-Hill, Inc., 1981, p. 362.) Despite exclusion from the
act, most agricultural lenders follow its spirit and intent.
A main provision of the Truth in Lending Act was that lenders must
calculate and show borrowers total finance charges over the life of the loan,
as well as the annual percentage rate (APR). The APR provides a common basis
to compare interest charges associated with the loan. The APR may or may not
be the same as the contractual rate (the rate actually stated on the loan contract). The difference between the two rates is due to the different methods
of computing the total interest charge.
Methods of Computation
Lenders use three major methods to calculate interest charges:
- the add-on method,
- the discount method, and
- the remaining balance method.
The first two methods are not commonly used by major agricultural lenders, but are used by finance companies that may make some agricultural loans.
Add-On Method
Under the add-on method, the lender calculates the total interest charge
by multiplying the entire loan amount by the contractual interest rate, and
then multiplying the total interest cost by the period (months, years) covered
by the loan. The interest charge is added to the principal to determine the
total amount to be repaid. This amount is then divided by the number of
repayment periods to determine each payment. The total interest charge is
thus: I = A x ic x N, where I = total interest charge over the life of the
loan, A = amount of loan, ic= contractual interest rate per time period, and N
= number of periods covered by the loan.
The periodic payment is: Bn = (A + I) / N, where B = total payment and n
= repayment periods under consideration.
For an example of add-on interest, assume a $3,000 loan to be repaid in
two annual installments. The annual contractual interest rate is 6 percent.
Then, the total interest charge is: I = $3,000 x .06 x 2 = $360 and the annual
payments will be: B = ($3,000 + 360) / 2 = $1,680.
Discount Method
The discount method calculates total interest the same way as the add-on
method, with one exception. The interest is subtracted from the loan amount
and the borrower receives the balance. The total interest charge is: I = A x
ic x N.
The amount the borrower receives is: L = A - I, where L=loan proceeds
and the periodic payment is: Bn = A / N. Using the same data as before ($3,000 loan amount, 6 percent annual
interest rate, over 2 years), the total interest charge is again $360: I =
$3,000 x .06 x 2 = $360.
The borrower would receive $2,640: L = $3,000 - $360 = $2,640 and would
repay two installments of $1,500 each: Bn = $3,000 / 2 = $1,500.
Remaining Balance Method
When the remaining balance method is used, the interest charge is
computed in each period by multiplying the contractual interest rate by the
principal balance remaining at the beginning of the period (the unpaid
balance). The major difference between this method and the previous two,
beyond the complexity of the mathematical calculations, is that interest is
not charged on principal that has been repaid.
The total interest charge, the periodic interest payment, and the
periodic principal payment all depend on the method selected for repayment.
Two methods are commonly used: the equal total payment plan (Standard plan)
and the equal total principal plan (Springfield plan). To illustrate interest
computation for these two repayment methods, assume a $10,000 loan at a 12
percent annual contractual rate to be repaid in eight annual payments.
Equal Total Payments. Under the equal total payment method, the annual
payment for this loan is $2,013.03 for each of the 8 years. This was
determined by multiplying the amortization factor (see Table 3) for 12 percent
interest and 8 year payment period times the loan amount. The portion of each
payment that is interest and the portion that is principal will vary with each
payment. At the end of the first year, interest is charged on the full $10,000
principal outstanding: I1 = $10,000 x 0.12 = $1,200.
Thus, the principal payment is the difference: C1 = $2,013.00 - $1,200 =
$813.00, where C = the principal payment.
The remaining principal balance after the first payment is: R1 = $10,000
- $813.00 = $9,187.00, where R = the principal balance.
Interest in the second year is charged on the remaining balance: I2 =
$9,187.00 x 0.12 = $1,102.44, which yields: C2 = $2,013 - $1,102.44 = $910.59
and R2 = $9,187.00 - $910.59 = $8,276.41.
A similar set of steps is followed each year thereafter.
Equal Principal Payments. Under the equal principal payment plan,
interest charges are calculated in a similar manner. The primary difference is
that equal principal payments are made. In addition, the annual total
repayments will decline each year due to a declining principal balance upon
which interest is calculated: I1 = $10,000 x 0.12 = $1,200.
But the principal payment is: C1 = $10,000 / 8 = $1,250. Thus, the total
payment for the first year is: B1 = $1,250 + $1,200 = $2,450 and the remaining
principal balance is: R1 = $10,000 - $1,250 = $8,750.
In the second year: I2 = $8,750 x 0.12 = $1,050, C2 = $1,250, B2 = $1,250
+ $1,050 = $2,300, and R2 = $8,750 - $1,250 = $7,500.
Comparison of Interest Charges
Given a contractual interest rate and the terms of the loan, total
interest charges will vary significantly. To illustrate, assume a $10,000 loan
is taken out at an annual contractual interest rate of 12 percent to be repaid
in annual payments over 8 years. Table 1 shows how the different methods of
computing interest charges affect the total interest cost.
The add-on and discount methods result in significantly higher interest
charges and APRs, thus, the contractual interest rates substantially
understate the true or annual percentage rate. In fact, the discount method
produces ridiculous results for a loan of 8 years. But this method usually is
used by finance companies only for short-term loans such as 30, 60 or 180
days. When either the add-on or discount method is used, lenders usually quote
an interest rate substantially lower than rates quoted by other lenders, thus
for short-term loans, the extremely high APR figures indicated in Table 1 will
not be correct. Few agricultural loans are written using these methods, but
some people may have Consumer loans that use either add-on or discount
interest.
| Table 1: Example of interest charge methods (principal $10,000, interest rate 12%, 8 annual payments). |
|
Add-On |
Discount |
Remaining Balance |
|---|
| Standard Plan |
Springfield Plan1 |
|---|
| Amount received |
$10,000 |
$ 400 |
$10,000 |
$10,000 |
| Total repaid |
19,600 |
10,000 |
16,104 |
15,400 |
| Total interest paid |
9,600 |
9,600 |
6,104 |
5,400 |
| Equal annual payments |
2,450 |
1,500 |
2,013 |
1,9252 |
| APR (percent) |
17.97 |
375.00 |
12.00 |
10.74 |
1 Remaining balance method with equal principal payment.
2 Average annual payment. |
| Table 2: APR under different maturity and service charge assumptions ($10,000 loan, 10% interest rate). |
| Service charge (% of loan amt) |
Length of loan repayment |
|---|
| 3 yr |
5 yr | 10 yr | 20 yr |
|---|
| 0 |
10.00 |
10.00 |
10.00 |
10.00 |
| 1 |
10.58 |
10.40 |
10.24 |
10.15 |
| 2 |
11.16 |
10.80 |
10.48 |
10.30 |
| 3 |
11.74 |
11.20 |
10.72 |
10.45 |
| 4 |
12.32 |
11.60 |
10.96 |
10.96 |
| 5 |
12.90 |
12.00 |
11.20 |
10.75 |
Service Charges and Stock Purchase Requirements
The APR stated for loans also should reflect all loan service costs
(such as loan origination fees, closing costs or points) and stock purchase
requirements (such as those of the Farm Credit Services). Table 2 shows an example of the effect of service charges on the APR for different loan
maturities. Note, as the maturity is lengthened, the effect of the service
charge is diminished.
Variable Interest Rates and Partial Year Loans
Interest rates usually are stated on an annual basis, but they are
sometimes quoted on a monthly or even on a weekly or daily basis. In fact,
most department store or bankcard charge accounts are stated on a monthly
basis. Consequently, it is important to determine the time period for which
the stated interest rate applies. Furthermore, even if an annual interest rate
is stated, the length of most agricultural operating loans is less than a full
year, and most credit card charges are paid off much more quickly than 1 year.
Partial Years
If interest is stated on an annual basis and is calculated using the
remaining balance method, but the loan is paid off in less than 1 year, the
amount of interest due can be calculated as: I = A x i (Number of months money
is used / 12) or I = A x im x (Number of days money is used / 365).
If interest is stated on a monthly basis (im), calculate interest as: I
= A x im x (Number of months money is used).
Variable Interest
In recent years, it has become common for lending institutions to adopt
a variable interest rate policy. Typically, the interest rate will be stated
on an annual basis and will not change more often than once each month. If
interest is calculated on the remaining balance method, it can be calculated
in a way similar to the process for partial year loans. For example, if the
interest rate was 12 percent for 2 months, 13 percent for 3 months and 14
percent for 7 months, the annual interest is: I = A x 0.12 x (2 / 12) + A x
0.13 x (3 / 12) + A x 0.14 x (7 / 12).
If applied to the add-on or discount methods, a new calculation would
have to be made each time the rate changed.
| Table 3: Amortization table. Annual principal and interest paid per $1 borrowed by length of loan and interest rate. |
| No. of annual payments |
Annual Interest Rate |
|---|
| 8.00% |
8.50% |
9.00% |
9.50% |
10.00% |
10.50% |
11.00% |
| 3 |
0.38803 |
0.39154 |
0.39505 |
0.39858 |
0.40211 |
0.40566 |
0.40921 |
| 4 |
0.30192 |
0.30529 |
0.30867 |
0.31206 |
0.31547 |
0.31889 |
0.32233 |
| 5 |
0.25046 |
0.25377 |
0.25709 |
0.26044 |
0.26380 |
0.26718 |
0.27057 |
| 6 |
0.21632 |
0.21961 |
0.22292 |
0.22625 |
0.22961 |
0.23298 |
0.23638 |
| 7 |
0.19207 |
0.19537 |
0.19869 |
0.20204 |
0.20541 |
0.20880 |
0.21222 |
| 8 |
0.17401 |
0.17733 |
0.18067 |
0.18405 |
0.18744 |
0.19087 |
0.19432 |
| 9 |
0.16008 |
0.16342 |
0.16680 |
0.17020 |
0.17364 |
0.17711 |
0.18060 |
| 10 |
0.14903 |
0.15241 |
0.15582 |
0.15927 |
0.16275 |
0.16626 |
0.16980 |
| 11 |
0.14008 |
0.14349 |
0.14695 |
0.15044 |
0.15396 |
0.15752 |
0.16112 |
| 12 |
0.13270 |
0.13615 |
0.13965 |
0.14319 |
0.14676 |
0.15038 |
0.15403 |
| 13 |
0.12652 |
0.13002 |
0.13357 |
0.13715 |
0.14078 |
0.14445 |
0.14815 |
| 14 |
0.12130 |
0.12484 |
0.12843 |
0.13207 |
0.13575 |
0.13947 |
0.14323 |
| 15 |
0.11683 |
0.12042 |
0.12406 |
0.12774 |
0.13147 |
0.13525 |
0.13907 |
| 20 |
0.10185 |
0.10567 |
0.10955 |
0.11348 |
0.11746 |
0.12149 |
0.12558 |
| 25 |
0.09368 |
0.09771 |
0.10181 |
0.10596 |
0.11017 |
0.11443 |
0.11874 |
| 30 |
0.08883 |
0.09305 |
0.09734 |
0.10168 |
0.10608 |
0.11053 |
0.11502 |
| 35 |
0.08580 |
0.09019 |
0.09464 |
0.09914 |
0.10369 |
0.10829 |
0.11293 |
| 40 |
0.08386 |
0.08838 |
0.09296 |
0.09759 |
0.10226 |
0.10697 |
0.11172 |
| No. of annual payments |
11.50% |
12.00% |
12.50% |
13.00% |
13.50% |
14.00% |
15.00% |
|---|
| 3 |
0.41278 |
0.41635 |
0.41993 |
0.42352 |
0.42712 |
0.43073 |
0.43798 |
| 4 |
0.32577 |
0.32923 |
0.33271 |
0.33619 |
0.33969 |
0.34320 |
0.35027 |
| 5 |
0.27398 |
0.27741 |
0.28085 |
0.28431 |
0.28779 |
0.29128 |
0.29832 |
| 6 |
0.23979 |
0.24323 |
0.24668 |
0.25015 |
0.25365 |
0.25716 |
0.26424 |
| 7 |
0.21566 |
0.21912 |
0.22260 |
0.22611 |
0.22964 |
0.23319 |
0.24036 |
| 8 |
0.19780 |
0.20130 |
0.20483 |
0.20839 |
0.21197 |
0.21557 |
0.22285 |
| 9 |
0.18413 |
0.18768 |
0.19126 |
0.19487 |
0.19851 |
0.20217 |
0.20957 |
| 10 |
0.17338 |
0.17698 |
0.18062 |
0.18429 |
0.18799 |
0.19171 |
0.19925 |
| 11 |
0.16475 |
0.16842 |
0.17211 |
0.17584 |
0.17960 |
0.18339 |
0.19107 |
| 12 |
0.15771 |
0.16144 |
0.16519 |
0.16899 |
0.17281 |
0.17667 |
0.18448 |
| 13 |
0.15190 |
0.15568 |
0.15950 |
0.16335 |
0.16724 |
0.17116 |
0.17911 |
| 14 |
0.14703 |
0.15087 |
0.15475 |
0.15867 |
0.16262 |
0.16661 |
0.17469 |
| 15 |
0.14292 |
0.14682 |
0.15076 |
0.15474 |
0.15876 |
0.16281 |
0.17102 |
| 20 |
0.12970 |
0.13388 |
0.13810 |
0.14235 |
0.14665 |
0.15099 |
0.15976 |
| 25 |
0.12310 |
0.12750 |
0.13194 |
0.13643 |
0.14095 |
0.14550 |
0.15470 |
| 30 |
0.11956 |
0.12414 |
0.12876 |
0.13341 |
0.13809 |
0.14280 |
0.15230 |
| 35 |
0.11760 |
0.12232 |
0.12706 |
0.13183 |
0.13662 |
0.14144 |
0.15113 |
| 40 |
0.11650 |
0.12130 |
0.12613 |
0.13099 |
0.13586 |
0.14075 |
0.15056 |
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