Explain the three reasons money now is worth more than the same amount later.
Look up the interest rate on the safest place you would actually keep spare money right now. That might be your bank's savings account or fixed deposit page, or the current Singapore Savings Bonds rate on the MAS website. Write the rate down. You need it to judge any offer that pays you more later in exchange for money now.
An old schoolmate messages you. He needs S$1,000 to cover a few weeks' rent while he changes jobs, and offers to repay S$1,100 in two years, "with interest, to be fair." It sounds generous, since you get back S$100 more than you handed over (1,100 - 1,000). The common mistake is to pick the bigger number. Choosing S$1,100 over S$1,000 treats a dollar in two years as equal to a dollar today, and it is not. The idea that money now and money later have different values is called time value of money, and this module is built on three separate reasons for it.
Money you hold today can go into a savings account, a fixed deposit or a government bond and earn a return. Money that arrives later misses those years of earning. If you lend the S$1,000, you give up the return you would otherwise have earned on it.
Say you could earn 3% a year (an example rate). Using the compounding from Lesson 2.1, "Simple interest pays on what you put in, compound pays on what you earned", S$1,000 grows to S$1,030 after one year and S$1,060.90 after two years. Lending the money means giving up S$60.90 of earnings. His S$1,100 is about S$39 more than S$1,060.90, so on this reason alone his offer still wins.
Module 4 showed that the same dollar buys less each year. Money you receive in the future gets spent at future prices. If prices rise 2.5% a year (an example rate), S$1,000 of goods today costs about S$1,050.63 after two years. Divide S$1,100 by 1.050625 and you get roughly S$1,047 of buying power at current prices, so the S$100 extra shrinks to about S$47 at today's prices.
Reasons one and two are different calculations. The first is about earning on money you hold now. The second is about losing buying power on money that arrives later. They often move together, but they are not the same thing, so work them out separately.
The third reason has nothing to do with rates: a future payment might never arrive. Your schoolmate could repay early if he finds a job quickly. He could repay late or in pieces if he struggles and asks for more time. He could also never repay at all, even with no bad intent. Money already in your account carries none of that doubt, while any future payment carries some amount of it.
How much doubt depends on who is promising. A bond issued by the Singapore Government carries almost none. A personal loan to a friend between jobs carries quite a lot. The same thinking applies to other promises, such as an employer bonus paid only if you stay two more years, a promised payout from an insurance plan, or an instalment a buyer owes you for a used car. Promises fail at some rate, so each of these is worth a little less than its face value.
The discount rate is the yearly rate you use to bring a future sum back to what it is worth today. It is one number that captures all three reasons: lost earnings, rising prices and the risk of not being paid. There is no official discount rate for your life, so choosing one is a judgement. A workable method:
Do not compare the raw amounts. Find the rate you could earn on a safe option you would actually use for this money. Check the product page, or the MAS website for Singapore Savings Bonds. Add points for the risk that the payment does not come: more for a shaky promise, less for a solid one. Use the result as your yearly discount rate. Grow today's sum at that rate to the future date, or bring the future sum back to today, and compare.
Try it on the schoolmate's offer. At a discount rate of 3%, S$1,000 grows to S$1,060.90 in two years. That is less than S$1,100, so his offer looks better than keeping the money. Now add three points for the risk that he struggles to repay, which gives 6%. At 6%, S$1,000 grows to S$1,123.60 in two years. That is more than S$1,100, so keeping the money wins. The friend and the offer are the same in both cases, and the answer flips because of the risk judgement alone.
Time value of money does not make the decision for you. You still decide what return you gave up and how far you trust the person paying you, and the arithmetic shows what those two decisions add up to. For longer periods and regular payments the sums get tedious, so Lessons 6.2 and 6.3 use spreadsheet functions to handle them.
Once you start looking, you'll find offers of less now or more later turn up more often than you might think: a discount for paying a year's subscription upfront, a bonus that vests later, a refund paid in instalments. Think of one you have faced recently, and before you work out any numbers, notice which of the three reasons weighs most on your choice.
Write down an offer where you could take less money now or more money later. Note which one you would take and why.
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