You will be able to explain how compounding frequency changes the effective yearly return on the same stated rate.
Two banks advertise the same 3% a year on a twelve-month deposit. You put S$10,000 in each. At the end of the year, one account holds S$10,300 and the other holds S$10,304.16. Nobody made a mistake, and neither bank hid a fee. The only difference is how often each one adds interest to your balance.
Four dollars is not going to change your life. The reason it appears at all is worth understanding, though, because the same mechanism costs you real money on a credit card or a loan.
A rate quoted per year does not tell you how often the interest is paid in. Some accounts credit interest once a year. Many savings accounts credit monthly, and some work it out daily and credit monthly. Each time interest is added, it starts earning interest of its own, as you saw in lesson 2.1, Simple interest pays on what you put in, compound pays on what you earned.
When interest is credited monthly, the bank does not pay 3% each month. It splits the yearly rate into twelve, so each month pays 3% divided by 12, which is 0.25%. On S$10,000, the first month adds S$25. The second month pays 0.25% on S$10,025, which is about S$25.06. Every month the base is a little bigger, so by month twelve the balance is S$10,000 times 1.0025 to the power of 12, about S$10,304.16.
With yearly crediting, there is one payment of 3% on S$10,000 at the end of the year: S$300 exactly, for S$10,300.
To compare accounts that credit at different frequencies, convert each into an effective annual rate, the yearly return you actually get once the compounding inside the year is counted. The formula is (1 plus the stated rate divided by n) to the power of n, minus 1, where n is the number of times interest is credited each year.
For 3% credited monthly, that is 1.0025 to the power of 12, minus 1, which is about 3.04%. Credited daily, using 365 periods, it is about 3.05%. Credited yearly, it is 3% exactly, because there is nothing to compound within the year.
So the effective annual rate tells you that 3% monthly is worth about 3.04% a year. Once two accounts are both expressed as effective annual rates, you can compare them directly, whatever their crediting schedules.
At low rates, crediting frequency barely matters. The difference between 3% and 3.04% on S$10,000 is S$4 a year. If one account pays a higher stated rate and credits yearly, it will usually beat a lower rate credited monthly, so frequency is rarely the deciding factor for savings.
The gap grows with the rate, which is why it matters on debt. Take a balance charged at 24% a year, a figure chosen for this example. Credited yearly, the effective cost is 24%. Charged monthly, at 2% a month, it is 1.02 to the power of 12, minus 1, which is about 26.82%. Worked out daily, it is about 27.11%. On a S$5,000 balance left unpaid for a year, monthly compounding at that rate costs about S$1,341 rather than the S$1,200 a reader of the headline would expect.
High-rate debt is usually charged daily or monthly, so the stated yearly rate understates what you pay. Module 3 goes further into how loans are priced, and the course Credit and debt: scores, cards, loans and BNPL covers card debt in detail.
When you compare two places to keep money, look in the product terms for three things: the stated yearly rate, how often interest is credited, and whether it is worked out on the daily balance or a monthly figure. Banks in Singapore publish this in their terms and conditions or the product's fact sheet. If an account only shows the rate, ask how often it is credited before you decide.
You now have a formula that turns any stated rate and any crediting frequency into a single yearly figure. Pick two accounts that quote the same rate but credit at different intervals, and work through the formula for each one.
Compare two accounts with the same stated rate, one crediting monthly and one yearly, and calculate the effective annual rate of each.
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