Sometimes, a little arithmetic can do what a long argument cannot. It can puncture a rather large financial assumption.
Consider a simple proposition raised by the defense in the impeachment case involving Vice President Sara Duterte. Substantial wealth could have been built simply by placing money in a bank time deposit, rolling over both principal and interest, and letting the magic of compounding do the work over the years.
The math is possible. But possible is not the same as plausible.
Suppose an initial time deposit grows to P500 million purely through compounding, with all interest earnings rolled back into the principal. At an average 12 percent net annual return, the depositor would need to start with roughly P51.8 million and leave it untouched for 20 years.
That is already a substantial sum. Shorten the horizon to 15 years, and the required starting deposit rises to about P91.3 million.
There is, however, a small catch hiding inside that seemingly generous 12 percent net return.
Because interest income is subject to a 20 percent tax, the underlying gross rate would have to be around 15 percent to produce a 12 percent net return.
That may look wonderfully convenient on paper. In the real Philippine financial market, however, sustaining a 15 percent gross return on an ordinary time deposit for 15 or 20 years is another matter entirely.
Time deposits are supposed to be boring. Asking one to compound at something approaching equity-market speeds for two decades is considerably less boring.
Now suppose we bring the gross rate down to a more modest 10 percent. After the 20 percent tax, that leaves an 8 percent net return. The required starting deposit then jumps to roughly P157.6 million for 15 years and P107.3 million for 20 years.
And that is before inflation enters the picture.
P500 million twenty years from now will not buy what P500 million buys today. The nominal figure may look impressive, but its real purchasing power will have been steadily eroded by rising prices. A deposit may be perfectly safe in nominal terms and still lose ground in real terms whenever its after-tax return does not comfortably beat inflation.
Then comes the more interesting question. Who would willingly park that kind of money in a time deposit for two decades?
A businessman with P157 million, or even P52 million, to deploy would presumably have more productive options. The money could expand an existing business, acquire property or other assets, or be invested in securities. Locking up the entire amount for years simply to earn a fixed return would come with a substantial opportunity cost.
The scenario becomes more plausible if the money belongs to an institution whose mandate is preservation of capital and predictable income, such as an insurance company or a trust fund manager. Even then, plausible does not mean probable.
The arithmetic, after all, is not merely doing arithmetic.
It is quietly asking a much bigger set of questions. Where did the money come from? Why was so much of it kept in a time deposit? Why for so long? And what more productive uses for that money were passed up along the way?
Those questions cannot be answered by the magic of compounding alone.
