You will be able to use a future value formula to see how returns change the monthly saving you need.
If you have tried a savings calculator on a bank website, you may have seen it give a lower monthly figure than the one you worked out by hand in lesson 1.1. The calculator assumes your savings earn a return while you wait. Part of the target then comes from growth, so less has to come from your own deposits. Whether that assumption is fair or dangerous depends on two things: how far away the goal is, and what rate the calculator used.
Take Mei and Daniel, the couple saving for their wedding in lesson 1.1. They need S$24,000 more in 30 months (the same made-up figures as lesson 1.1). With no return, that is S$800 a month.
If their savings earn 2% a year, credited monthly, the figure drops to about S$780.83 a month. That saves them about S$19 a month, roughly S$575 over the 30 months. It's pleasant to have, and it does not change their plan. They still need to find close to S$800 every month.
This holds for most short goals of two or three years. Interest on a balance that starts small and grows month by month adds up to a small share of the target, so nearly all of the target comes from your own deposits. If a short-goal plan, such as a wedding or a car downpayment, only works because of the return, the plan does not work.
Now suppose you start from nothing and want S$60,000 in ten years (an example figure). At 0%, you need S$500 a month, which is S$60,000 / 120 months.
At 2% a year, credited monthly, you need about S$452.08 a month. Over the ten years your own deposits come to about S$54,250 and interest makes up about S$5,750. At 4% a year, you need about S$407.47 a month, and your own deposits come to about S$48,900 in total. Between 0% and 4% the difference is close to S$93 a month, which is more than S$11,000 of your own money over the period.
The gap comes from time. Each early deposit has many years to earn returns of its own, which you saw in How money works lesson 6.2, "Future value: what a sum or monthly saving grows to". On a long goal, the return starts to carry real weight.
There is a catch. Higher rates usually come from assets whose value can fall, which module 2 covers. A long horizon lets returns do more of the work, and it also leaves more room for returns to come in lower than planned.
Excel and Google Sheets both have a PMT function, which gives the payment needed to reach a target. You type =PMT(rate per period, number of periods, present value, future value). For a monthly plan, the four inputs are:
Rate per period: the yearly rate divided by 12. Number of periods: the number of months. Present value: what you have already saved, entered as a negative number, or 0 if you have nothing yet. If you have S$5,000 already saved, enter it as minus 5,000. Future value: your target.
For the ten-year goal at 2%, =PMT(2%/12, 120, 0, 60000) gives minus 452.08. The answer is negative because money you pay in carries a minus sign, and FV works the same way, as shown in How money works lesson 6.2. Read the negative result as the monthly payment you need to make. Money you have already saved goes into present value as a negative number for the same reason: it also goes in from your side.
Before you trust the formula with a real rate, run it at a zero rate. =PMT(0, 120, 0, 60000) gives minus 500, which matches the plain division of S$60,000 by 120 months. If your zero-rate result does not equal the target divided by the number of months, something in the formula is wrong. Once it matches, run it again with a cautious rate and compare the two results. The difference shows how much of the target the return is carrying.
Two mistakes come up often. The first is mixing periods, for example putting in a yearly rate with a number of months. This makes the payment look tiny. When the periods are months, always divide the rate by 12. The second is reading the minus sign as an error and flipping the inputs around until the answer looks positive. This can leave present value with the wrong sign, and the payment you get will be wrong.
Plan with a cautious rate. If the money for the goal will sit in cash or cash-like places, use a rate at or below what those places pay today. Rates on savings accounts and short-term bonds change, so today's rate may not last the whole period. If a long goal will be invested, use a rate well below what you hope to earn.
The reason is what happens when you're wrong. If you plan on a cautious rate and the actual return comes in higher, you reach the target early or have money left over, and that spare money can move to your next goal. If you plan on a high rate and it comes in low, you find out near the date, when the only fixes left are borrowing or delaying.
For any goal under about three years, a zero rate is a perfectly good choice. It keeps the arithmetic honest, and compared with a small positive rate it costs you only a few dollars a month, as Mei and Daniel's S$19 shows.
In the activity, take one of your own goals that is at least several years away and run PMT twice, once at zero and once at a cautious rate, so you can see how much of the target the return would really be carrying.
Pick one long goal and use PMT to work out the monthly saving twice: once at a zero return and once at a cautious rate.
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