Consumer Credit Transactions - PPS

Consumer Credit Transactions

Assurant Continuing Education


Overview of Carleton Financial Computations43 Years of Experience providing credit math

solutionsIn today’s market primarily a software companyClients include Banks, Finance Companies, Auto

Dealers/Financiers, Credit Insurance Companies, System Providers (Partners)

The breadth of our client base allow us to see the “Universe” of computations, approaches, policies, and choices made by creditors.

Carleton served as a member of the Federal Reserve Board “Industry Advisory Panel” during the creation of the Truth-in-Lending Act in 1968 and again with the “Simplification” process 10 years later.

Carleton got a “head start” on the complexities of computing the new required value “APR”


Because the “consumer credit math” is so specialized, much of it is open to interpretation by the user. To think there is a “universal formula” that ‘everybody’ uses is a simplistic and inaccurate view of the landscape.

Embrace the concept that calculations are “different” rather than instantly “wrong” if the resulting numbers are not identical.


Communication is vital to understanding the principles and concepts of Consumer Credit Math

Use and Misuse of labels adds a layer of confusion atop an already complex subject.

For instance, the terms:

1. “APR”2. “Principal” 3. “Service Charge”4. “Actuarial Method”


CONSUMER CREDIT

Credit dispersed for personal or household consumption. As opposed to ‘Commercial Credit’ which is B2B.

Loans vs. SalesClosed End Credit – fixed duration/ number of

payments.


Four Principle Elements of a Credit Transaction

AmountRateTerm / No. PmtsPayment

Generally, if you know 3 of these elements, you can solve for the 4th.


To fully understand a consumer credit transaction, you need to understand the concept of

Amortization

“the gradual reduction of a debt by means of equal periodic payments sufficient to meet current interest

and liquidate the debt at maturity.”

– Dictionary of Banking and Finance


The process of amortization is illustrated by a schedule of payments that shows the allocation of each payment to interest and principal.

Theoretically speaking, the principal balance should be $0.00 after the final scheduled payment has been made at maturity.


Amortization Schedules can be devised to follow various concepts, so the key to understanding all the

numbers on the page are “what are the rules?”

Does interest accrue:1) Actuarial/Simple Interest2) Rule of 78ths3) Pro-rata


“One Formula to Rule Them All”

I = P x R x T

Interest = Principal x Rate x Time


The key is clear communication and understanding of:

P = What is included in the principal amount?

R= What type of rate is it?

T= Time; The critical wildcard in the equation


$1,000 Loan

10%

Begin Bal. Int. Prin. End Bal.

$1,000.00 $ 8.33 $79.58 $ 920.42

$920.42 $ 7.67 $80.24 $840.18

Payment = $87.91

Rate = 10% simple annually

12 Monthly Payments


Begin Bal. Int. Prin. End Bal.

$1,000.00 $ 8.33 $79.58 $ 920.42

$ 920.42 $ 7.67 $80.24 $840.18

I = P x R x T

Interest = $1,000 x .10 x 1/12 = $8.3333


Principal Rate Term

$ 1,000.00 10% 12

Beginning Payment Interest Principal Ending Balance Balance

920.42 87.91 7.67 80.24 840.18

840.18 87.91 7.00 80.91 759.27

759.27 87.91 6.33 81.58 677.69

677.69 87.91 5.65 82.26 595.43

595.43 87.91 4.96 82.95 512.48

512.48 87.91 4.27 83.64 428.84

428.84 87.91 3.57 84.34 344.50

344.50 87.91 2.87 85.04 259.46

259.46 87.91 2.16 85.75 173.71

173.71 87.91 1.45 86.46 87.25

87.25 87.91 0.73 87.18 0.07

Consumer Credit Transactions Amortization Process

The full precision amortizing payment for this data is:

87.91588723This value represents the “Math” involved in computing

the present value to find the payment amount.


The actual transaction charge is $54.92 A “real world” adjustment must be made to

account for the $.07 difference.The mathematically amortizing payment for this

data is $87.91588723. However, that amount cannot be physically collected.

The payment here is “truncated” to $87.91.The “mills” of $.00588723 are truncated off the

full precision payment.$.00588723 x 12 = $.07064676


The rounding of the monthly payment has a profound effect on the return/yield/APR of the transaction.

If the payment is truncated (low rounded) to $87.91,

the APR is 9.9873415%If the payment is high rounded to $87.92, the APR is

10.0088428%If the “Max APR” is 10%, does the $87.92 represent a

violation?


FINANCING CALCULATIONS

Loan Amount/Sales Price

Interest RateTerm/No. PmtsPayment Amount

TILA DISCLOSURE

APRFINANCE CHARGEAMOUNT FINANCEDTOTAL OF PMTS/

TOTAL SALE PRICE


It is important to note that the Truth-in-Lending Act does not care:How large a value the APR is.How interest accrues on the loan. The “Fed

Calendar” is designed to “level the field”.What rates are used for ancillary products.


The bottom line is that the TILA APR is a “back end” number derived once all the

other values have been computed.

Mis-use of labels promotes confusion for the intended purpose of many disclosure items.


Truth-in-Lending Definitions

Amount Financed – amount disbursed to or on behalf of the consumer.

Finance Charge – Cost of credit as a dollar amount.

Total of Payments – The sum of the amount financed and finance charge.

APR – Cost of credit as a yearly percentage.


Principal Amount Amount to which the interest rate is applied to arrive at the interest charge.

Amount Financed The amount disbursed to or on behalf of the consumer.

What the “Amount Financed” is NOT is: “The total amount financed in the contract.”


In any Credit Transaction*

Amount Financed Principal+ Finance Charge + Interest Total of Pmts Total of Pmts

*Excluding the instance where outstanding balance “MOB” insurance or debt protection is included.


Constructing a Transaction

Loan Proceeds $1,000.00Single Credit Life Pr 11.25Loan Fee 30.00

Principal Amount $1,041.25 (value used to compute interest) Less Loan Fee 30.00Amount Financed $1,011.25

Interest Amount $45.59 Plus Loan Fee 30.00Finance Charge $75.59

Interest Rate 8.00% amortizes principal amount produces interest amount

A.P.R. 13.52% amortizes amount financed produces finance charge

Loan Proceeds $1,000.00

Single Credit Life Pr 11.25

Loan Fee 30.00

Principal Amount $1,041.25

Less Loan Fee 30.00

Amount Financed $1,011.25

Interest Amount $45.59

Plus Loan Fee 30.00

Finance Charge $75.59

Total of Payments $1,086.8420 Pmts @ $90.57Interest Rate 8.00%Amortizes Principal amount produces interest amountAPR 13.52%Amortizes Amount Financed produces Finance Charge

Constructing a Transaction

Constructing a TransactionAmortization of a Loan

Principal Rate Term1,041.25$ 8% 12

Begin Balance Payment Interest Principal Ending Balance1,041.25 90.57 6.94 83.63 957.62

957.62 90.57 6.38 84.19 873.43 873.43 90.57 5.82 84.75 788.68 788.68 90.57 5.26 85.31 703.37 703.37 90.57 4.69 85.88 617.49 617.49 90.57 4.12 86.45 531.04 531.04 90.57 3.54 87.03 444.01 444.01 90.57 2.96 87.61 356.40 356.40 90.57 2.38 88.19 268.21 268.21 90.57 1.79 88.78 179.43 179.43 90.57 1.20 89.37 90.06

90.06 90.57 0.60 89.97 0.09

Amortization of a LoanAdding a Penny to the Payment

Principal Rate Term1,041.25$ 8% 12

Begin Balance Payment Interest Principal Ending Balance1,041.25 90.58 6.94 83.64 957.61

957.61 90.58 6.38 84.20 873.41 873.41 90.58 5.82 84.76 788.65 788.65 90.58 5.26 85.32 703.33 703.33 90.58 4.69 85.89 617.44 617.44 90.58 4.12 86.46 530.98 530.98 90.58 3.54 87.04 443.94 443.94 90.58 2.96 87.62 356.32 356.32 90.58 2.38 88.20 268.12 268.12 90.58 1.79 88.79 179.33 179.33 90.58 1.20 89.38 89.95

89.95 90.58 0.60 89.98 (0.03)

Parameters that shape the characteristics of a credit transaction:

Add-on InterestSimple / Actuarial Interest

Discount InterestRevisiting;

I = P x R x T

Consumer Credit TransactionsInterest Computation

Methods

Add-On Interest

Add-on is expressed as “dollars per hundred dollars per year” or $12 per $100 per year is equivalent to what is called “12% add-on”.

It is computed on the original principal amount for the full term of the loan as though there were no installments.

Add-on was extremely popular before the prevalent use of computers due to ease of use using the I = P x R x T formula. A payment can be computed with only pencil and paper.

The Add-on method calculates precomputed interest.


Example: $5,000 loan,

12% add-on interest rate, 36 month loan term

I = $5,000 x .12 x 36/12 = $1,800 interest$5,000 principal+ $1,800 interest

$6,800 Total of Pmts / 36 = $188.8888888 Mo. Pmt

Consumer Credit Transactions Add-On

Interest

However, a “real world” adjustment needs to be made. The $1,800 represents theoretical interest at 12% add-on. The lender cannot collect a payment of $188.888888.

Adjusting the payment to $188.88 produces new disclosure values.

$188.88 x 36 = $6,799.68 Total of Pmts - 5,000.00 Principal $1,799.68 Interest Chg


Interest

The Truth-in-Lending Annual Percentage Rate using a payment of $188.88 is 21.196435%

The nominal simple interest equivalent or “APR rate” for 12% add-on at 36 months is generally listed as 21.20% in printed publications.

If the payment were rounded up to $188.89, then the resulting TILA APR would be 21.200324%


Interest

Add-on Rate Term Simple Rate

12% 6 20.29%

12% 12 21.46%

12% 18 21.64%

12% 24 21.57%

Consumer Credit Transactions “Rate Book“

Conversions

Add-on Rate Term Simple Rate

12% 6 20.2880308%

12% 12 21.4571854%

12% 18 21.6426446%

12% 24 21.5712782%

Consumer Credit Transactions “Rate Book“

Conversions

The predominance of credit contracts in today’s market are computed with a simple interest rate. This type of interest is often called “actuarial interest” to distinguish it from add-on interest.

Whereas add-on interest is computed on the initial principal amount for the full term of the transaction, simple interest also utilizes

I = P x R x T but uses the average principal balance.

Consumer Credit Transactions Simple/Actuarial

Interest

Consumer Credit Transactions Process of

Amortization

Sum of Outstanding Principal Balances

$6,599.30

$6,599.30 / 12 = $549.94166666= average balance

I = $549.941666 x .10 x 12/12=$54.99416

Discount interest is computed using I=PxRxT and like Add-on computes a charge for a stated time period and disregards repayment.

“Principal” with Discount interest is the total of payments. Thus, there is inherent compounding aka “interest on interest” associated with Discount interest.

Consumer Credit Transactions Discount Interest

Discount Interest Example$1,000 “face amount”10% Discount Interest24 Month Term

I = $1,000 x .10 x 24/12 = $200 Interest Charge


The $200 precomputed interest charge

must be subtracted from the

“face amount” to arrive at the proceeds.

$1,000 - $200 = $800 proceeds/amount financed

However, a “real world” adjustment needs to be made if equal payments are desired.


$1,000 / 24 pmts = $41.666666

If the payment is truncated to $41.66, then the “face amount” needs to be adjusted to

$999.84 (24 x $41.66) and a new interest charge computed.

I = $999.84 x .10 x 24/12 = $199.968


Many small loan rate structures charge differing rates based on specific loan balances.

Most of these structures are, or were, part of the Uniform Consumer Credit Code. These are referred to as “code” states.

The highest interest rate is applied to the lowest balance.


Melded/Graduated Rates

It is important to note that this is a single transaction with all rates integrated into the amortization. It is NOT a simultaneous liquidation of three separate loans.

The key is that the “low rate” money liquidates first, and the “high rate” money liquidates last.



Example Transaction36% Per Annum of the Principal to $300 plus

21% of the excess to $1,000 plus15% of the remainder

$1,500 Principal12 Monthly Payments

Monthly Payment = $142.64Original Uniform Consumer Credit Code

UCCC



Consumer Credit Transactions Melded/Graduated

RatesSER Simple

Equivalent Rate

Two types of structures for interest in consumer credit transactions:

Precomputed Interest – The consumer contractually agrees to pay the “Total of Payments”. Interest is “precomputed” and figured into that amount.

Interest Bearing (aka “simple interest”) – Interest accrues on the principal balance as it is outstanding “from time to time”.

Precompute vs. Interest Bearing

Borrower agrees to repay “48 payments of $275.25” or a Total of Payments of $13,212.00

The only “rate” that appears on the contract is the Truth-in-Lending A.P.R.

Interest accrues according to the payments as originally scheduled.

A “Delinquency” or “Late” Charge is generally contracted for and collected to compensate for late payments.

A Refund or Rebate of unearned interest is necessary upon prepayment in full.

Characteristics of “Precompute”

Borrower agrees to repay the principal amount plus interest at a stated interest rate.

The computational interest rate is included in the promissory note language.

Interest accrues on the actual outstanding principal balances.

Payment habits influence the principal balance at any point in time.

The “net payoff” is the principal balance as of the last payment date

plus accrued interest from that date up to the payoff date of the loan.

No refund of interest is necessary. However, other charges such as

single premium credit insurance may require a refund when the loan is

paid in full.

Interest Bearing aka “Simple Interest“ Transactions

Front End – Loan OriginationAt the time of loan origination, the disclosure calculations

must be made under the assumption that all payments will be made on scheduled due dates and in scheduled amounts.

Back End – Loan Payment ServicingDuring repayment, the timing of payments and the specific

amounts of payments made will directly influence the net payoff balance of the loan.

Distinguishing between “Front End” and “Back End” Operations.

Interest Bearing

Precomputed



Loan Fee 30.00


Less Loan Fee 30.00



Plus Loan Fee 30.00


Total of Pmts $1,086.84

Precomputed vs. Interest Bearing

Historically, Industrial Loan Statutes have allowed fees for administering the back end processing of the loan. Typically these fees are called “maintenance fees” as a cost of maintaining the loan account.

TN and GA have such provisions and the AL Small Loan Statue now also allows such a fee.

Maintenance fees are typically a dollar charge per month.

The inclusion of an account maintenance fee introduces a new value to a transaction: “Face Amount”.

Industrial Loan Maintenance Fees

Loan Proceeds $1,000.00Single Credit Life Pr 11.25Loan Fee 30.00Principal Amount $1,041.25 Less Loan Fee 30.00Amount Financed $1,011.25Interest Amount $45.59 Plus Loan Fee 30.00Finance Charge $75.59Total of Pmts $1,086.84Add a maintenance fee of $3.00 per month/payment


The addition of maintenance fees introduces a new value into the anatomy of a credit transaction:

“FACE AMOUNT”The “Face Amount” is the sum of the original principal plus the

interest amount. Thus, it is one of the exceptions to the Principal + Interest = Total of Payments Rule.

The Maintenance Fee is simply an “add-on” to the P&I payment amount.

It is indeed a “Cost of Credit” so it must be included in the Truth-in-Lending Finance Charge.

The Maintenance Fee is added in at the “back end” of the transaction calculations.



Payment (P&I) $90.57

Interest $45.59

Plus Loan Fee $30.00

Plus Maint. Fee $36.00




Before Maintenance Fee

After Maintenance Fee



Loan Fee 30.00


Less Loan Fee 30.00



Plus Loan Fee 30.00


Total of Pmts $ 1,086.84

12 Pmts @ $90.57

TILA APR13.52%


(12 P&I Pmts @ $90.57)

Less Loan Fee 30.00



Plus Loan Fee 30.00

Plus Maint. Fee 36.00



12 Pmts @ 93.57

Less Maint. Fee 36.00

FACE AMOUNT $1,086.84

TILA APR 19.78%


Interest Rate 8.00%



Loan Fee 30.00


Less Loan Fee 30.00



Plus Loan Fee 30.00



12 Pmts @ $90.57

TILA APR 13.52%

Anatomy of a Credit Transaction

Consumer Credit Transactions - PPS

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