3.2.20 Indicating the Annual Effective Rate (TEA) for loans

The Annual Effective Rate of interest is computed in the following manner:

Annual Effective Loan Rate (TEA) = [[{1 + (i * PPI/360)} power (360/PPI)] / (1-or)] – 1

(In this case we have used 360 as the denominator. The other options available are 365 days, Actuals or Currency. The denominator is defaulted from your specification in the Branch Conditions screen. )

Where the following are the abbreviations used

• TEA – Annual Effective Loan Rate
• i - Annual Nominal Rate
• PPI – Interest payment periodicity
• or – Other surcharges expressed in percentage

Note:

The financial charges that are not recurring, for example a flat commission charged to disbursement, are accumulated and divided by the principal amount and are included in that percentage in the ‘or’ term.

The TEA can be used for reporting in customer statements and to regulatory authorities. For printing the effective loan rate in customer advices and central bank reports you can enable the Effective Loan Rate option.

Additionally, you also need to enable this option in the MM/Loans and Deposits Branch Conditions screen.

The TEA rates are calculated during:

• Takedown
• Value Dated Amendments
• Contract amendments resulting in change of cash flows
• Partial or full liquidation or pre-payment
• Rollover

Example 1

Case I

Mr. Franco Gonzalvis borrowed a sum of USD 10,000 under a Loan Scheme wherein the interest is paid by the borrower at the beginning of every month, while the principal is repaid at the end of the loan tenure. The bank charged a nominal interest of 12% p.a. Mr. Franco Gonzalvis availed of the loan on 1^st Jan 2002 and agreed to repay the entire principal on 1^st Jan 2003. The Bank charged a processing fee of USD 100 .In this case the TEA calculation is as follows:

[[{1 + (i * PPI/360)} power (360/PPI)]/(1-or)] – 1

PPI or the interest payment periodicity = Duration of the contract (365 days) divided by the number of interest payments (12). (that is, 365 / 12)

Therefore the above formula TEP=

[[{1 + (.12 * (365/12)/360)} power (360/(365/12))]/(1-.01)] – 1 = 0.138198

Note:

PPI is always computed as the duration of the Contract (deposit) divided by the number of interest payments (Even if the interest payment periods are not at periodic intervals.

Case II – Prepayment of Entire Loan Amount

Suppose Mr. Gonzalvis repays the entire Loan amount on 02-Dec-2002. Then the TEA computation Repayment of the loan is as follows:

The number of days between 1^st Jan 2002 and 02 Dec-2002 =335

The number of interest payments = 12 (11 monthly payments from 1^st Feb to 1^st Nov and an interest payment on 2^nd Dec for one day). Therefore PPI= 335/12

Thus TEP =

[[{1 + (.12 * (335/12)/360)} power (360/(335/12))]/(1-.01)] – 1=0.138254

Example 2

Rate Change

Mr. Marco Van Basten borrowed a sum of USD10000 under the Loan scheme wherein the interest payments are made by the borrower on the first of every month. He borrowed the sum on the 1^st of Jan 2002 when the rate was 12%. The loan repayment date is 1^st Jan 2003. After 2 months on the 1^st of March the rate changes to 15% (the terms of the loan– that is, interest payment periodicity remain unaltered). Other surcharges are waived. (that is, OS is zero)

In such cases the Nominal interest that is to be used in the above mentioned formula is computed as follows:

Nominal Interest Rate = Interest Paid /Average Deposit amount

= ((10000*0.12*2/12) + (10000*0.15*10/12))/10000

=1450/10000

=14.5%

The TEA for the above example =

[[{1 + (.145 * (335/12)/360)} power (360/ (335/12))]/ (1-0)] – 1=0.155022=15.5022%

Derivation of Nominal trate in case of Discounted or true discounted deposits In case of Discounted and True discounted deposits the Nominal rate of Interest is computed as follows:

Nominal Rate = (Interest Payable x 360)/((Principal-Interest Payable) x Duration of contract)

(In case of discounted and true discounted the duration of the contract is equal to the interest payment periodicity)

The Nominal Rate so computed is then used to compute TEA.

Example 3

Discounted Loan

Mr. Andrez Sacoli borrowed a sum of USD 10000 under a Discounted Loan Scheme. At the time of the initiating the loan the prevailing interest rate was 12% for a loan of one year. ). Other surcharges are waived. (that is, OS is zero)

TEA is computed as follows:

The nominal Rate = (1200 x 360)/ (10000 –1200) x 365 =13.449564%

TEA= [[{1 + (.13449564 * (335/12)/360)} power (360/ (335/12))]/ (1-0)] – 1

=0.134375 = 13.4375%

Example 4

True Discounted Loan

In the case of a True discounted loan the computation is as follows:

The Nominal Rate = (1071.43 x 360)/ (10000 –1071.43) x365= 0.118356 = 11.8356%

TEA= [[{1 + (.118356 * (335/12)/360)} power (360/ (335/12))]/ (1-0)] – 1 = 118263 = 11.8263%

Note:

In addition to enabling this option for the loan product you need to enable it for your branch through the MM/OL Branch Conditions screen.

For further details refer to the Automatic Processing chapter of this manual