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How Much Does It Cost?

How long will it take to save? Contributions and compound interest

The formulas to work out time to your goal or the monthly contribution needed, with examples and no promises of returns.

Updated: 6 minOCLUS Agency

To plan your saving you need a goal, what you already have, how much you put in each month and, if the money earns interest, the annual rate.

Without interest

Months = (goal − current savings) ÷ monthly contribution

To reach 6,000 starting from 1,200 and saving 300 a month: (6,000 − 1,200) ÷ 300 = 16 months.

With compound interest

With a monthly rate r (annual rate ÷ 12), the balance after n months, contributing C at the end of each month, is:

B = P × (1 + r)ⁿ + C × ((1 + r)ⁿ − 1) ÷ r

Solving for n gives the time needed; solving for C gives the monthly contribution to hit a deadline:

n = ln((Goal × r + C) ÷ (P × r + C)) ÷ ln(1 + r)
C = (Goal − P × (1 + r)ⁿ) × r ÷ ((1 + r)ⁿ − 1)

Example

Goal 10,000, current savings 1,000, 300 a month and 2% a year (r = 0.02 ÷ 12 ≈ 0.001667). The formula gives about 29.1 months, so 30 months rounded up. Without interest it would be exactly 30 months: over short periods compound interest adds little; its effect grows with time.

Caveats

  • No future return is guaranteed; use 0% if you don’t have a confirmed rate.
  • Tax and fees reduce returns: use the net rate.
  • Inflation erodes the purchasing power of your goal over time.

Try your own numbers in the savings calculator. This is not financial advice.

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