You will be able to use the FV function to project a lump sum and a regular monthly saving.
A bank's website has a savings calculator. You type in S$200 a month and five years, and it shows a figure with a growth chart. A financial adviser's slide shows another figure for the same saving. An app shows a third. They are all doing the same arithmetic under different assumptions, and once you can do it yourself, you can check any of them in under a minute.
This lesson gives you that arithmetic, first by hand and then with the FV function in Excel or Google Sheets. Every rate here is an example, not a forecast of what any product will pay.
Future value is what a sum will be worth at a later date once it has grown at a given rate. For a single sum that compounds once a year, the formula is the one from module 2: the sum times (1 plus the rate) to the power of the number of years.
Take S$10,000 at 3% a year for 10 years. That is 10,000 times 1.03 to the power of 10. 1.03 to the power of 10 is about 1.3439, so the future value is about S$13,439. The extra S$3,439 is ten years of interest, each year's interest earning interest of its own from then on.
You can do that on a phone calculator. Regular monthly savings are harder, because every deposit has a different number of months to grow. The first S$200 grows for five years, the last one for almost none. Adding up sixty separate calculations by hand is where the spreadsheet earns its place.
Excel and Google Sheets both have the same function:
FV(rate per period, number of periods, payment per period, present value)
The rate is the rate for one period. The number of periods is how many times that rate is applied. The payment is what you add every period, and the present value is what you start with. Both the payment and the present value are optional; put 0 for the one you are not using.
For the lump sum above, type =FV(3%, 10, 0, -10000). The periods are years, there is no regular payment, and the starting S$10,000 goes in as a negative. The answer is S$13,439.16, which matches the hand calculation.
The minus sign follows a rule the spreadsheet uses for every function in this module. Money you pay in is negative, money you get back is positive. You hand over S$10,000, so it is negative; the S$13,439.16 comes back to you, so FV shows it as positive. If you type the starting sum as a positive number, FV still works but shows the answer as negative, which is easy to misread. Lesson 3.4, Calculate the EIR of a flat rate offer with the RATE function, used the same convention.
The second rule is that the rate and the number of periods must use the same period. When you save monthly, the period is a month. Divide the yearly rate by 12 and multiply the years by 12. At 3% a year for five years, the rate per period is 3%/12, which is 0.25% a month, and the number of periods is 60.
Dividing by 12 assumes the stated yearly rate is credited monthly. As lesson 2.2, Monthly compounding beats yearly at the same stated rate, showed, 0.25% a month works out to a little over 3% a year once it compounds, about 3.04%. That small gap is why a calculator using monthly steps and one using yearly steps can disagree by a few dollars. Neither is wrong; they assume different crediting.
Say Priya, 27, puts aside S$200 a month for five years, with figures made up for the example, and earns 3% a year credited monthly. Type =FV(3%/12, 60, -200, 0). The answer is S$12,929.34. She paid in 60 times S$200, which is S$12,000, so S$929.34 is interest.
FV assumes each payment goes in at the end of the month. If you save at the start of each month instead, add a fifth argument of 1, and the result is slightly higher, about S$12,961.67, because each deposit gets one more month of growth.
Now suppose she already has S$5,000 saved when she starts. FV handles both in one formula: =FV(3%/12, 60, -200, -5000). The answer is S$18,737.43. Of that, about S$5,808 is the original S$5,000 grown for five years, and the rest is the monthly savings. One check worth doing: if you put the S$10,000 lump sum through monthly periods, =FV(3%/12, 120, 0, -10000), you get S$13,493.54 rather than S$13,439.16. The extra S$54 is the monthly crediting at work, not an error.
When you set this up yourself, put the rate, the monthly amount and the years in separate cells and point the FV formula at them, so that changing the rate or the time span means changing one cell rather than retyping the formula. Long periods are where the results start to surprise people, and comparing a low rate with a higher one over the same years shows why the time a sum is left to grow matters as much as the rate.
Use FV to project what S$300 a month grows to over 10, 20 and 30 years at 2% and 5% a year.
Junxiong-WFG Organisation is an authorised representative of AIA Financial Advisers Private Limited (Reg. No. 201715016G).