You will be able to calculate simple and compound interest by hand and explain why the gap widens over time.
Two friends each put S$10,000 aside at 25 and leave it alone. Both earn 4% a year, a rate chosen for this example. One takes the interest out every year and spends it on a holiday. The other leaves it in. For the first few years their balances look almost the same, and the friend spending the interest feels no worse off. By the time they are 45, one has S$18,000 counting the interest already spent, and the other has close to S$21,900. Same sum, same rate, same twenty years.
The gap comes from one difference: whether interest earns interest. That is the difference between simple and compound interest, and this lesson shows you how to work out both by hand.
With simple interest, you earn interest only on the money you first put in. The formula is the principal times the rate times the number of years.
S$10,000 at 4% for one year earns S$10,000 times 0.04, which is S$400. Over five years it earns S$400 a year for five years, S$2,000 in total, so the balance is S$12,000. Over twenty years it is S$400 times 20, or S$8,000, for a balance of S$18,000.
Each year adds the same S$400, because the interest is always worked out on the same S$10,000. On a chart, simple interest is a straight line.
With compound interest, each year's interest is added to the balance, and the next year's interest is worked out on the new, bigger balance.
Year one looks identical: S$10,000 times 1.04 is S$10,400. In year two, the 4% applies to S$10,400, so you earn S$416, not S$400, and the balance is S$10,816. The extra S$16 is interest on last year's interest. In year three you earn 4% of S$10,816, and so on.
You can do this step by step, multiplying by 1.04 once for each year, or use the short form: the starting sum times (1 plus the rate) to the power of the number of years. For twenty years at 4%, that is S$10,000 times 1.04 to the power of 20. A phone calculator gives about 2.1911 for the 1.04 part, so the balance is about S$21,911.
Simple interest after twenty years: S$18,000. Compound: about S$21,911. That is the S$21,900 from the two friends.
Put the two methods side by side and watch the difference between them, with the same S$10,000 at 4%.
After one year there is no gap. Both balances are S$10,400. After two years the gap is S$16. After five years, simple gives S$12,000 and compound about S$12,167, a gap of about S$167. After ten years it is S$14,000 against about S$14,802, a gap of about S$802. After twenty, it is the S$3,911 you saw above. Run it to thirty years and simple interest reaches S$22,000 while compounding reaches about S$32,434, a gap of more than S$10,000.
The gap does not grow evenly. It took ten years to reach about S$800 and the next twenty to pass S$10,000. That is because compound growth adds a percentage of a balance that is itself growing, while simple growth adds a fixed amount each year.
This shape is the reason starting earlier tends to beat adding more later. The years that do the most work are the last ones, and you only get them if the money started early enough to reach them. Someone who starts at 25 gets those late, steep years before 55. Someone who starts at 35 with the same sum and rate reaches 55 with the curve still at the flatter part.
Most savings accounts and fixed deposits in Singapore pay interest that is credited to your account, and if you leave it there, it compounds. Some products pay out interest instead of adding it, such as a bond paying a coupon into your bank account, and in that case the investment itself behaves like simple interest unless you reinvest the payments yourself. The two friends were in the same account; the only difference was what each did with the interest.
Compounding works against you on debt in exactly the same way. Unpaid interest added to a loan or card balance starts to attract interest of its own. Module 3 comes back to this when you look at what a loan really costs.
Spreadsheets will do all of this for you, and you will build one in lesson 2.4, Build a compounding table in a spreadsheet. Working a few years by hand first is still worth the ten minutes, because it shows you what the spreadsheet is doing and lets you spot a formula that has gone wrong. Use the two methods above, one multiplication at a time, on a smaller sum and a lower rate.
Work out by hand what S$5,000 becomes after 1, 5 and 10 years at 3% a year, first with simple interest and then with yearly compounding.
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