The illusion with numbers

Question: When I ask friends which 12-month loan to take between one charging 0.99 percent per month and another charging 14 percent per year, they tell me to take the 14-percent one because the other is on compounding and the 14 percent per year is not. Can you help enlighten me on this?

Answer: Numbers are complex concepts. And because the human brain generally does not want to analyze too much, it will resort to the simplest tool in its arsenal to interpret numbers, sometimes leading to magical results. Here is an example.

Pick a three-digit number with none of the digits repeating. Copy the number and reverse the order of the digits. Subtract the number with the lower value from the one with a higher value. Whatever the difference is, copy it and reverse the order of the digits of the copied number. If you end up with just a two-digit difference before reversing the order of digits, add zero to the start of that difference and then reverse the order of its digits. This time around, add the arrived at difference to its reversed digit order version and I will magically tell you at the end what will be your answer.

Simple, absolute and cumulative interest means the same thing. For our purpose, let us just use the term simple. On the other hand, effective, annualized and compounded annual interest also means the same thing. And for our purpose, let us just use the term effective.

Money you are holding onto today is worth more than money you will receive in the future, say a year from now. That is because you can use the money you will receive today and make it earn until that time that you are to receive money in the future. And from another point of view, with inflation, you can buy more with money that you will receive now than with money you are still to receive in the future. That is why in computing interest rate, it is important to take into consideration the time value of money. And for such computation, we also use as convention interest rates measured on a per year (annum) basis.

In addition, compounding means that whatever interest income a lender earns, that income will be reinvested at the quoted effective rate for the loan over the period of time that loan remains outstanding. In MS Excel, the syntax is =rate (nper,pmt,pv) where “nper” is the number of periods (e.g. years) or term of the loan, “pmt” is payment or the periodic interest income received by the lender and “pv” (expressed as a negative number as it is a cash outflow) is the present value or net amount of loan released. If payment is on a monthly basis, multiply the answer by 12 and express in percent form. Now, if the loan specifies a one-time payment, the syntax to use is =rate(nper,0,pv,fv) where “fv” is future value or the one-time payment that will be due. To get the annual rate, divide 365 by the number of days between loan release and payment dates then express in percent form.

So, from the point of view of the lender, if the loan interest were 0.99 percent per month or 11.88 percent per year (i.e. 0.99 percent x 12) for a term of 12 months, that implies that the lender should earn exactly 11.88 percent only if he were to reinvest all of his interest income at the same 11.88 percent per year (i.e. by relending them to someone else). But herein lies the secret.

When a loan is quoted at a low rate and on a monthly basis, more often than not, it is computed only on a simple basis. And for seemingly low interest rates quoted on a monthly basis, this is called add-on rate. This method applies the 0.99 percent interest per month to the original loan all of the time. The implication of this method is that the lender is relending his interest income to just one borrower and no one else, even if the borrower is not contracting additional loans. Also, the method of computing interest initially seems inequitable as interest is always based on the original loan principal, even when that loan principal is being paid down.

To avoid further nosebleed, suffice it to say that a 0.99-percent per month simple interest is equivalent to an effective interest of 21.25 percent per year. And that interest has yet to input any upfront loan processing fees that would reduce the amount of loan disbursement. The 0.99 percent per month interest is quoted only to magically make a high interest loan appear inexpensive, a mere marketing gimmick.

All loans can be computed on an effective basis with interest based on diminishing principal balance. And by the Truth in Lending Act, lenders are required to disclose all of the costs involved in the loans they offer, which means quoting the effective interest rate.

So, whenever you are borrowing, always ask the lender for the effective interest rate per year with all costs included like loan processing fee, convenience fee, collection fee and perhaps even coffee (if they are charging you for it).

Oh, by the way, the number you computed from our earlier exercise was 1,089, right? INQSend questions via “Ask a Friend, Ask Efren” free service at personalfinance.ph, SMS, Viber, Twitter, LinkedIn, WhatsApp, Instagram and Facebook.