F A M & A N H S E E S EONOMS alculatig loa iterest o. 3.758 y Nora L. Dalsted ad Paul H. Gutierrez Quick Facts... The aual percetage rate provides a coo basis to copare iterest charges associated with the loa. The cotractual rate is the iterest rate actually stated o the loa cotract. Leders use the add-o ethod, the discout ethod ad the reaiig balace ethod to calculate iterest charges. Agricultural leders do ot cooly use the first two ethods. The aual percetage rate stated for loas also should reflect all loa service costs ad stock purchase requireets. terest rates usually are stated o a aual basis, but soeties are quoted othly, weekly or daily. olorado State Uiversity ooperative Extesio. 9/9. Ay tie oey is borrowed, iterest is charged. How iterest is coputed ofte is cofusig, as is the aer i which the iterest rate is stated. The federal Truth i Ledig Act of 968 (ad its successor, the Truth i Ledig Siplificatio ad efor Act of 980) was eacted i order to assure a eaigful disclosure of credit ters ad to protect the cosuer agaist iaccurate ad ufair credit billig ad credit card practices. The act iposes detailed reportig requireets o leders. However, agricultural trasactios are fully excluded fro its applicatio. (Uchta, D.L., J. W. Looey, N.G.P. Krausz, ad H.W. Haah, Agricultural Law: Priciples ad ases. New York: McGraw-Hill, c., 98, p. 36.) Despite exclusio fro the act, ost agricultural leders follow its spirit ad itet. A ai provisio of the Truth i Ledig Act was that leders ust calculate ad show borrowers total fiace charges over the life of the loa, as well as the aual percetage rate (AP). The AP provides a coo basis to copare iterest charges associated with the loa. The AP ay or ay ot be the sae as the cotractual rate (the rate actually stated o the loa cotract). The differece betwee the two rates is due to the differet ethods of coputig the total iterest charge. Methds of oputatio Leders use three ajor ethods to calculate iterest charges:. the add-o ethod,. the discout ethod, ad 3. the reaiig balace ethod. The first two ethods are ot cooly used by ajor agricultural leders, but are used by fiace copaies that ay ake soe agricultural loas. Add-O Method Uder the add-o ethod, the leder calculates the total iterest charge by ultiplyig the etire loa aout by the cotractual iterest rate, ad the ultiplyig the total iterest cost by the period (oths, years) covered by the loa. The iterest charge is added to the pricipal to deterie the total aout to be repaid. This aout is the divided by the uber of repayet periods to deterie each payet. The total iterest charge is thus: = A x i c x N =total iterest charge over the life of the loa A =aout of loa i c = cotractual iterest rate per tie period N=uber of periods covered by the loa
The periodic payet is: = (A + ) / N =total payet =repayet periods uder cosideratio For a exaple of add-o iterest, assue a $3,000 loa to be repaid i two aual istallets. The aual cotractual iterest rate is 6 percet. The, the total iterest charge is: = $3,000 x.06 x = $360 ad the aual payets will be: = ($3,000 + 360) / = $,680 Discout Method The discout ethod calculates total iterest the sae way as the add-o ethod, with oe exceptio. The iterest is subtracted fro the loa aout ad the borrower receives the balace. The total iterest charge is: = A x i c x N The aout the borrower receives is: L = A - L=loa proceeds ad the periodic payet is: = A / N Usig the sae data as before ($3,000 loa aout, 6 percet aual iterest rate, over years), the total iterest charge is agai $360: = $3,000 x.06 x = $360 The borrower would receive $,640: L = $3,000 - $360 = $,640 ad would repay two istallets of $,500 each: = $3,000 / = $,500 eaiig alace Method Whe the reaiig balace ethod is used, the iterest charge is coputed i each period by ultiplyig the cotractual iterest rate by the pricipal balace reaiig at the begiig of the period (the upaid balace). The ajor differece betwee this ethod ad the previous two, beyod the coplexity of the atheatical calculatios, is that iterest is ot charged o pricipal that has bee repaid. The total iterest charge, the periodic iterest payet, ad the periodic pricipal payet all deped o the ethod selected for repayet. Two ethods are cooly used: the equal total payet pla (Stadard pla) ad the equal total pricipal pla (Sprigfield pla). To illustrate iterest coputatio for these two repayet ethods, assue a $0,000 loa at a percet aual cotractual rate to be repaid i eight aual payets. Equal Total Payets. Uder the equal total payet ethod, the aual payet for this loa is $,03.03 for each of the 8 years. This was deteried by ultiplyig the aortizatio factor (see Table 3) for percet iterest ad 8 year payet period ties the loa aout. The portio of each payet that is iterest ad the portio that is pricipal will vary with each payet. At the ed of the first year, iterest is charged o the full $0,000 pricipal outstadig: = $0,000 x 0. = $,00 Thus, the pricipal payet is the differece: = $,03.00 - $,00 = $83.00
=the pricipal payet The reaiig pricipal balace after the first payet is: = $0,000 - $83.00 = $9,87.00 =the pricipal balace terest i the secod year is charged o the reaiig balace: = $9,87.00 x 0. = $,0.44 Which yields: = $,03 - $,0.44 = $90.59 ad = $9,87.00 - $90.59 = $8,76.4 A siilar set of steps is followed each year thereafter. Equal Pricipal Payets. Uder the equal pricipal payet pla, iterest charges are calculated i a siilar aer. The priary differece is that equal pricipal payets are ade. additio, the aual total repayets will declie each year due to a decliig pricipal balace upo which iterest is calculated. = $0,000 x 0. = $,00 ut, the pricipal payet is: = $0,000 / 8 = $,50 Thus, the total payet for the first year is: = $,50 + $,00 = $,450 Ad the reaiig pricipal balace is: = $0,000 - $,50 = $8,750 the secod year: = $8,750 x 0. = $,050 = $,50 = $,50 + $,050 = $,300 = $8,750 - $,50 = $7,500 Table : Exaple of iterest charge ethods (pricipal $0,000, iterest rate %, 8 aual payets). Add-O Discout eaiig alace Stadard Pla Sprigfield Pla Aout received $0,000 $ 400 $0,000 $0,000 Total repaid 9,600 0,000 6,04 5,400 Total iterest paid Equal aual payets 9,600 9,600 6,04 5,400,450,500,03,95 AP (percet) 7.97 375.00.00 0.74 eaiig balace ethod with equal pricipal payet Average aual payet. opariso of terest harges Give a cotractual iterest rate ad the ters of the loa, total iterest charges will vary sigificatly. To illustrate, assue a $0,000 loa is take out at a aual cotractual iterest rate of percet to be repaid i aual payets over 8 years. Table shows how the differet ethods of coputig iterest charges affect the total iterest cost. The add-o ad discout ethods result i sigificatly higher iterest charges ad APs, thus, the cotractual iterest rates substatially uderstate the true or aual percetage rate. fact, the discout ethod produces ridiculous results for a loa of 8 years. ut this ethod usually is used by fiace copaies oly for short-ter loas such as 30, 60 or 80 days. Whe either the add-o or discout ethod is used, leders usually quote a iterest rate substatially lower tha rates quoted by other leders, thus for short-ter loas, the extreely high AP figures idicated i Table will ot be correct. Few agricultural loas are writte usig these ethods, but soe people ay have cosuer loas that use either addo or discout iterest.
Table : AP uder differet aturity ad service charge assuptios ($0,000 loa, 0% iterest rate). Service charge % of loa at) Legth of loa repayet 3 yr 5 yr 0 yr 0 yr 0 0.00 0.00 0.00 0.00 0.58 0.40 0.4 0.5.6 0.80 0.48 0.30 Service harges ad Stock Purchase equireets The AP stated for loas also should reflect all loa service costs (such as loa origiatio fees, closig costs or poits) ad stock purchase requireets (such as those of the Far redit Services). Table shows a exaple of the effect of service charges o the AP for differet loa aturities. Note, as the aturity is legtheed, the effect of the service charge is diiished. 3.74.0 0.7 0.45 4.3.60 0.96 0.96 5.90.00.0 0.75 Variable terest ates ad Partial Year Loas terest rates usually are stated o a aual basis, but they are soeties quoted o a othly or eve o a weekly or daily basis. fact, ost departet store or bakcard charge accouts are stated o a othly basis. osequetly, it is iportat to deterie the tie period for which the stated iterest rate applies. Furtherore, eve if a aual iterest rate is stated, the legth of ost agricultural operatig loas is less tha a full year, ad ost credit card charges are paid off uch ore quickly tha year. Partial Years f iterest is stated o a aual basis ad is calculated usig the reaiig balace ethod, but the loa is paid off i less tha year, the aout of iterest due ca be calculated as: = A x i (Nuber of oths oey is used / ) or = A x i x (Nuber of days oey is used / 365) f iterest is stated o a othly basis (i ), calculate iterest as: = A x i x (Nuber of oths oey is used) Variable terest recet years, it has becoe coo for ledig istitutios to adopt a variable iterest rate policy. Typically, the iterest rate will be stated o a aual basis ad will ot chage ore ofte tha oce each oth. f iterest is calculated o the reaiig balace ethod, it ca be calculated i a way siilar to the process for partial year loas. For exaple, if the iterest rate was percet for oths, 3 percet for 3 oths ad 4 percet for 7 oths, the aual iterest is: = A x 0. x ( / ) + A x 0.3 x (3 / ) + A x 0.4 x (7 / ) f applied to the add-o or discout ethods, a ew calculatio would have to be ade each tie the rate chaged.
Table 3: Aortizatio Table -- Aual Pricipal ad terest Paid per $ borrowed by Legth of Loa ad terest ate. No. of aual payets Aual terest ate 8.00% 8.50% 9.00% 9.50% 0.00% 0.50%.00%.50%.00%.50% 3.00% 3.50% 4.00% 5.00% 3 0.38803 0.3954 0.39505 0.39858 0.40 0.40566 0.409 0.478 0.4635 0.4993 0.435 0.47 0.43073 0.43798 4 0.309 0.3059 0.30867 0.306 0.3547 0.3889 0.333 0.3577 0.393 0.337 0.3369 0.33969 0.3430 0.3507 5 0.5046 0.5377 0.5709 0.6044 0.6380 0.678 0.7057 0.7398 0.774 0.8085 0.843 0.8779 0.98 0.983 6 0.63 0.96 0.9 0.65 0.96 0.398 0.3638 0.3979 0.433 0.4668 0.505 0.5365 0.576 0.644 7 0.907 0.9537 0.9869 0.004 0.054 0.0880 0. 0.566 0.9 0.60 0.6 0.964 0.339 0.4036 8 0.740 0.7733 0.8067 0.8405 0.8744 0.9087 0.943 0.9780 0.030 0.0483 0.0839 0.97 0.557 0.85 9 0.6008 0.634 0.6680 0.700 0.7364 0.77 0.8060 0.843 0.8768 0.96 0.9487 0.985 0.07 0.0957 0 0.4903 0.54 0.558 0.597 0.675 0.666 0.6980 0.7338 0.7698 0.806 0.849 0.8799 0.97 0.995 0.4008 0.4349 0.4695 0.5044 0.5396 0.575 0.6 0.6475 0.684 0.7 0.7584 0.7960 0.8339 0.907 0.370 0.365 0.3965 0.439 0.4676 0.5038 0.5403 0.577 0.644 0.659 0.6899 0.78 0.7667 0.8448 3 0.65 0.300 0.3357 0.375 0.4078 0.4445 0.485 0.590 0.5568 0.5950 0.6335 0.674 0.76 0.79 4 0.30 0.484 0.843 0.307 0.3575 0.3947 0.433 0.4703 0.5087 0.5475 0.5867 0.66 0.666 0.7469 5 0.683 0.04 0.406 0.774 0.347 0.355 0.3907 0.49 0.468 0.5076 0.5474 0.5876 0.68 0.70 0 0.085 0.0567 0.0955 0.348 0.746 0.49 0.558 0.970 0.3388 0.380 0.435 0.4665 0.5099 0.5976 5 0.09368 0.0977 0.08 0.0596 0.07 0.443 0.874 0.30 0.750 0.394 0.3643 0.4095 0.4550 0.5470 30 0.08883 0.09305 0.09734 0.068 0.0608 0.053 0.50 0.956 0.44 0.876 0.334 0.3809 0.480 0.530 35 0.08580 0.0909 0.09464 0.0994 0.0369 0.089 0.93 0.760 0.3 0.706 0.383 0.366 0.444 0.53 40 0.08386 0.08838 0.0996 0.09759 0.06 0.0697 0.7 0.650 0.30 0.63 0.3099 0.3586 0.4075 0.5056