How this calculator works
This is a savings timeline for a single purchase: a trip, a car, a deposit on a home or anything else with a price. The starting balance earns interest every month, and the monthly deposit is added at the end of each month. The calculator finds the first month in which the balance is at least the price and rounds up, because you cannot usually buy in a fraction of a month. The interest is calculated on the balance as it grows, so the total you deposit is less than the price by the amount of interest earned. A higher rate shortens the timeline, but it also means taking more risk with money you plan to spend soon. For a goal within a few years, a savings account or short-term deposit is usually the better fit than an investment that can fall. The model assumes a constant rate and no tax, fees or price inflation. If the thing you want rises in price, add the expected increase to the target.
Formula
With i = annual rate / 12 and monthly deposits D, the balance after n months is P(1+i)^n + D((1+i)^n - 1)/i. Solve for n: n = ln((G + D/i) / (P + D/i)) / ln(1+i), where G is the price. At a zero rate, n = (G - P)/D. Months to save is n rounded up, total deposited is P + D x months, and interest earned is G - total deposited.
Worked example
A $15,000 goal with $2,000 already saved and $300 a month at 5% a year takes 39 months, about 3.25 years. You will deposit $2,000 + 39 x $300 = $13,700 and earn $1,300 of interest. At $400 a month, the same goal takes 30 months and you deposit $14,000.
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Frequently asked questions
Should I use a savings rate or an investment return?
Use a savings rate for a goal within about three years, because the money needs to be there when you need it. Use a long-run investment return only for a distant goal, and accept that the actual result can be much lower.
What if the price rises with inflation?
Add the expected price increase to the target. For example, if the item costs $15,000 now and you expect 3% a year for four years, the target becomes $15,000 x 1.03^4 = $16,882.
Why is the total deposit less than the price?
Because the balance earns interest along the way. The gap is the interest earned, which is the price minus everything you deposited, including the starting balance.
Can I save weekly instead?
The calculator uses monthly deposits. A weekly plan can be modelled by multiplying the weekly amount by 52 and dividing by 12 to get an equivalent monthly figure, though the timing of interest credits will differ slightly.