# How add-on-rate, 5-6 loans work.

Byline: Efren Ll. Cruz

QUESTION: When a loan is on add-on-rate or 5-6, does this mean the loan is not based on diminishing balance?-asked at Ask a friend, ask Efren free service available at www.personalfinance.ph and Facebook.

Answer: Firstly, allow me to issue a correction to my previous article entitled, The broader meaning of P/E. The term earnings in the price-to-earnings ratio or P/E refers to the company's net income as of a certain date divided by the total number of stockholders' shares (and not just the number of stockholders as one stockholder can own more than one share) also as of the same date.

Now, let us tackle your question. Assume you were offered a P100,000 loan computed on add-on-rate or AOR with a repayment period of 12 months. Let us also assume the lender quoted an AOR of 0.99 percent a month.

Given the said parameters, if you were to avail of the loan, your monthly amortization would be P9,323.33. The amortization was arrived at in two parts: monthly principal repayment = availed loan amount divided by 12 months monthly interest payment = 0.99 percent always multiplied to the availed loan amount As to your question on whether an AOR loan is not based on diminishing balance, the answer is yes. But wait, the effective interest on an AOR loan is also not the quoted rate of 0.99 percent a month. Neither is the effective interest on an AOR loan derived from simply multiplying the monthly rate by 12 months or, in this case, 11.88 percent per year (i.e. 0.99 percent x 12)

If you want to compute the effective interest rate on an AOR loan, you will need to convert the loan amortization schedule to one that uses diminishing balance. More specifically, you will have to derive the interest rate using the loan availment of P100,000, the term of 12 months and the monthly amortization of P9,323.33.

Fortunately, spreadsheet calculators already incorporate the formula for computing effective interest rates. In any spreadsheet calculator (e.g. MS Excel, Numbers), simply key in the following syntax =rate(12,-9323.33,100000) exactly as is and then hit enter. The answer should be 1.7707 percent. But that is a monthly rate since we used a monthly amortization. To get the effective annual interest, simply multiply the derived monthly rate by 12 and you get about 21.25 percent p.a.

The rule in borrowing is that you are supposed to pay interest only on the balance of the loan that you have not repaid. That is why interest computed on diminishing balance gives you the effective interest because your loan principal balance gets paid down periodically. AOR just presents the interest rate in a different fashion that makes the rate appear low.

For its part, a 5-6 loan implies an annual simple interest rate of 20 percent. This is because you will have to repay the P5 you borrowed with P6. The difference, when divided by the P5 loan is the 20 percent interest. The only thing is that in 5-6 loans, you are required to pay in periods much shorter than one year, sometimes even in just a matter of days, with the absolute value of the interest staying the same.

And since money paid now is worth more than money paid later (i.e. the time value of money), you are effectively charged a much higher interest rate.

To demonstrate, assume you borrow P1,000. Under a 5-6 loan, the absolute interest would be P200 (i.e. 1,000 x 20 percent). The lender will then ask you to pay P30 a day for 40 days. Why? Because P30 a day multiplied by 40 days equals P1,200. When compared to your loan amount of P1,000, the difference of P200 equates to the same absolute interest.

We can also use our time value of money spreadsheet formula to arrive at the effective interest. Just key in the following syntax =rate(40,-30,1000) exactly as is and then hit enter. The answer should be 0.9209 percent. And since the answer is a daily rate, let us multiply it by 360 (days in a year). The answer comes to a whopping equivalent of 332 percent a year.

If you do not have a spreadsheet calculator, you can simply download the country's first free personal finance mobile app called Ya!man and use the loan calculator module to compute effective interest on loans presented on diminishing balance, AOR and 5-6. Ya!man also allows you to ask personal finance questions via SMS free of charge.

So the next time you borrow, remember that you can always ask the lender for the true cost of the loan. After all, that is part and parcel of the disclosure required under the Truth in Lending Act. Then you can validate his answer by computing the effective interest rate yourself.

As a final note, include any loan processing fees in the computation as these fees tend to push up the effective interest rate. In the spreadsheet formula, you are to deduct the loan processing fees from the amount of loan availed and keep the amortization as is.

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