Effective Annual Interest Rate in Topping Up Your eMoney or eWallet

I am a bit intrigued to think about the top up fee that we need to pay to replenish our eMoney or eWallet, for example, I found the example, where we need to pay Rp 1,000 for each top up transaction. Since this world is driven by interest, which is the mother of economy, then I guess, somehow I should relate this top up fee to interest that I have to pay implicitly.

How to do this?

Let’s say, the case is:

• we want to top up Rp 300,000 with a top up fee Rp 1,000.
• we replenish this top up every two weeks, meaning that Rp 300,000 will be used up to buy food, transportation, etc.

So how much is the implicit effective annual interest rate that we need to pay:

The analysis is shown below.

The implicit effective annual interest rate is 8.43%. This seems to me quite high since this is not too far from working capital borrowing interest rate, though we don’t borrow anything from anybody, as that’s pretty much our own money.

I will go further by having sensitivity analysis with one-factor change, that is the replenished amount, and keep the remaining assumption constant.

Sensitivity (1) One Factor : The Replenished Amount (IDR)

The chart below demonstrated that the effective annual interest rate will fly from 62% for replenished amount of Rp 50,000 declining to near to 5% for the replenished amount of Rp 500,000. This will mean that the higher amount that we replenished, then the lower effective annual interest rate that we need to pay for this top up transaction.

How about if we keep all assumptions constant, but the frequency of the top up?

Sensitivity (2) One Factor : The Frequency of the Top Up (in Days)

From the above chart, we could see that the longer days that we do this top up transaction, then the interest will decline from near 30% (if we fill up the top up every 5 days) to near 2% (for every 60 days) with the amount of Rp 300,000 every time we top up the emoney or ewallet.

How about if we make the amount of the replenishment and the frequency of the top up becoming variable?

Sensitivity (3) Two Factors : The Replenished Amount (IDR) and the Frequency of the Top Up (Days)

The above table gave us that the effective annual interest rate is quite far by wide margin. If we top up Rp 50,000 every 5 days, then the interest rate will be 324%…wow is this really what we paid?

If we top up Rp 500,000 every 2 months (+/- 60 days), then the interest is around 1,18%, this sounds very low.

So what we could get something out of this analysis:

1. All fees that we pay, there is implicit effective annual interest rate that we need to pay to the service provider.
2. The top up fee of Rp1,000 may sound small money, but when we link that fee to the frequency of the top up transactions and the amount being replenished, that small amount might give us interest rate that shoots through the roof.
3. The old adage will ring again, watch your spending habits. My two-cents suggestion: drive your car till it drops!

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