Calculate simple and compound interest by hand, and explain why the gap between them grows wider each year.
Open your phone calculator and key in S$10,000 x 0.04. You should get S$400. That is what S$10,000 earns in one year at 4% a year (example figures chosen for this example). The same two numbers are used in every calculation that follows, so keep the calculator out and check each one as you read.
Simple and compound interest differ in only one way: whether the interest you have already earned goes on to earn more. Once you can do both by hand, you can check any interest figure a bank or a spreadsheet shows you by working it out yourself and comparing.
The principal is the money you put in at the start. Simple interest is paid on that principal and nothing else, and its formula is principal x rate x number of years.
Before you multiply anything, turn the percentage into a decimal: 4% is 0.04. Multiply the principal by that decimal to get one year's interest: S$10,000 x 0.04 = S$400. Multiply the yearly figure by the number of years you're looking at to get the total interest. For 5 years that's S$400 a year x 5 = S$2,000. Add the total back onto the principal, and the balance after 5 years is S$12,000.
Over 20 years the interest comes to S$400 x 20 = S$8,000, leaving a balance of S$18,000. At 30 years the balance reaches S$22,000. Each year adds exactly S$400, since the calculation always starts from the same S$10,000. If you plotted the balance on a chart you would get a straight line.
Compound interest works differently. At the end of each year the interest is added to the balance, and the following year's interest is worked out on that bigger figure.
The year-by-year method is one multiplication per year. Add the rate to 1 to get your multiplier, which at 4% is 1.04. For year 1, S$10,000 x 1.04 = S$10,400, which is exactly what simple interest gives after one year. For year 2, multiply S$10,400 by 1.04. The interest this time is 4% of S$10,400, or S$416 instead of S$400, and the balance moves to S$10,816. The extra S$16 is interest earned on year 1's interest. Year 3 starts from S$10,816: take 4% of it, or multiply it by 1.04. Keep going like this, once for every further year.
Twenty multiplications get tedious, so there is a shorter route. Raise 1 plus the rate (here 1.04) to the power of the number of years, which any phone calculator can do, and multiply the starting sum by the answer. Over 20 years that's S$10,000 x 1.04^20. Since 1.04^20 is about 2.1911, the balance comes to about S$21,911.
If you line the two methods up, you can see that the gap between them does not widen at a steady pace:
after 1 year, both stand at S$10,400 and there is no gap after 2 years, compound is ahead by S$16 after 5 years, S$12,000 simple against about S$12,167 compound, a gap of about S$167 after 10 years, S$14,000 against about S$14,802, a gap of about S$802 after 20 years, S$18,000 against about S$21,911, a gap of S$3,911 after 30 years, S$22,000 against about S$32,434, a gap of more than S$10,000 (about S$10,434)
It took ten years for the gap to reach about S$800, and the following twenty years took it past S$10,000. The difference comes from how each method adds money. Simple interest adds a fixed sum every year. Compound interest adds a percentage of a balance that keeps rising, so each year's addition is a bit larger than the one before. The final years of compounding add the most, and your money only gets to them if it was put in early enough.
Take two friends. At 25, each sets aside S$10,000 in the same account at 4% a year, and neither touches it. One takes the interest out every year and spends it on a holiday, so that money earns simple interest. The other leaves the interest in, so it compounds. For the first few years their balances are close, and the friend taking holidays feels no worse off. By 45, that friend's total is S$18,000, counting the interest already spent, while the friend who left it alone has close to S$21,900. Both had the same sum, the same rate and the same twenty years. The only difference was what each did with the interest.
The age you begin at matters for the same reason, and starting earlier usually does better than adding more later. Someone who begins at 25 reaches the late, steep part of the curve before turning 55. Someone who begins at 35, with the same sum at the same rate, turns 55 while their curve is still in its flatter part.
For each product you hold, find out what happens to the interest. Most savings accounts in Singapore credit it to your account, and if you leave it there it compounds. A fixed deposit is handled at maturity instead. At DBS, for example, the principal and interest are renewed automatically for the same tenor at the interest rate on offer then, unless you give the bank other instructions at least 1 working day before maturity. So a fixed deposit's interest goes on earning interest only if it is renewed together with the principal. If you take the interest out, it stops compounding. Check your own bank's maturity instructions to see what yours will do. Some other products pay the interest out to you instead of adding it to the balance. A bond is one example: its interest payment, called the coupon, is paid into your bank account. A product like this behaves like simple interest unless you reinvest the payments yourself.
Compounding works against you on money you owe. When unpaid interest on a loan or credit card is added to the balance, that interest starts being charged interest too. Module 3 comes back to this when it looks at what a loan really costs.
A spreadsheet can do all of these calculations, and you'll build one in Lesson 2.4, "Build a compounding table in a spreadsheet". Before you get there, spend about ten minutes working out a few years by hand. Once you have done the multiplications yourself, you'll know what the spreadsheet is doing and you'll be able to tell when a formula has gone wrong.
Pick a smaller sum and a lower rate. Work out a few years using both methods above, one multiplication at a time.
Take S$5,000 at 3% a year. Work out by hand what it becomes after 1, 5 and 10 years with simple interest, then do the same with yearly compounding.
Junxiong-WFG Organisation is an authorised representative of AIA Financial Advisers Private Limited (Reg. No. 201715016G).