You will be able to use a future value formula to see how returns change the monthly saving you need.
You open a savings calculator on a bank's website, type in a goal, and it tells you a monthly figure lower than the one you worked out by hand in lesson 1.1, because the calculator has assumed your savings earn a return while they wait, so part of the target comes from growth and less has to come from you.
That can be a fair assumption or a dangerous one. It depends on how far away the goal is and what rate the calculator used. This lesson shows you how to do the same sum yourself, so you can see how much work the return is really doing.
Take Mei and Daniel's wedding from lesson 1.1, with the same made-up figures. They need S$24,000 more in 30 months. With no return at all, that is S$800 a month.
Now suppose the money earns 2% a year, credited monthly. The monthly figure drops to about S$780.83. Over 30 months, the return saves them about S$19 a month, roughly S$575 in all. That is pleasant but it doesn't change the plan.
This is true of almost every short goal. Over two or three years, interest on a growing balance adds up to a small share of the target, so nearly all of it comes from what you put in. If your plan for a wedding or a car downpayment only works because of the return, the plan does not work.
Stretch the horizon and the picture changes. Say you start from nothing on a goal that needs S$60,000 in ten years, again with figures made up for the example.
At a zero return, you need S$500 a month: S$60,000 divided by 120 months.
At 2% a year, credited monthly, you need about S$452.08 a month. Over ten years you put in about S$54,250, and interest makes up the other S$5,750 or so.
At 4% a year, you need about S$407.47 a month, and you put in about S$48,900 in total.
So over ten years, the difference between 0% and 4% is close to S$93 a month, or more than S$11,000 of your own money. The gap comes from time: as How money works lesson 6.2, Future value: what a sum or monthly saving grows to, showed, each deposit made early has many years to earn returns of its own.
There is a catch. The higher rate usually comes from assets whose value can fall, which module 2 deals with. A long horizon lets returns do more of the work, and it also leaves more room for those returns to come in lower than you planned.
You don't need to do any of this by hand. Excel and Google Sheets both have a PMT function that gives the payment needed for a target:
PMT(rate per period, number of periods, present value, future value)
For a monthly saving plan, the rate per period is the yearly rate divided by 12, and the number of periods is the number of months. The present value is what you have already saved, and the future value is your target.
For the ten-year goal at 2%, type =PMT(2%/12, 120, 0, 60000). The answer is minus 452.08. It is negative for the same reason FV showed negative answers in How money works lesson 6.2: money you pay in carries a minus sign. If you already had S$5,000 saved, you would put it in as minus 5,000 for the present value, because that money also goes in from your side.
Check the zero case too. With a rate of 0, =PMT(0, 120, 0, 60000) gives minus 500, which matches the plain division. That is a quick way to make sure you have typed the formula correctly before trusting it with a real rate.
Which rate should go into the plan? A cautious one. If a goal's money will sit in cash and cash-like places, use a rate at or below what those places pay today, and remember that rates on savings accounts and short-term bonds change. If a long goal will be invested, use a rate well below what you hope to earn.
The reason is simple. If the actual return comes in higher, you reach the target early or with money left over. That is a bonus, and you can move the spare money to the 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.
A zero rate is a perfectly good choice for any goal under about three years. It keeps the arithmetic honest and costs you only a few dollars a month compared with a small positive rate.
Two mistakes catch people with PMT. The first is mixing periods: a yearly rate with a number of months, which makes the payment look tiny. Always divide the rate by 12 when the periods are months. The second is reading the minus sign as an error and flipping the inputs until the answer looks positive, which can leave the present value with the wrong sign.
In the activity you'll 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.
Use PMT to compare the monthly saving needed for one long goal at a zero return and at a cautious rate.
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