Calculator of Alexandria

Savings goal calculator

Work out how much to save each month to reach a savings goal by a deadline, with interest and money already saved included.

A high-yield savings account, say. Use 0 if it sits in cash.

Save each monthDD
Total you put in
Interest earned

Formula

D=(G−P(1+i)n) i(1+i)n−1D = \frac{(G - P(1+i)^n)\,i}{(1+i)^n - 1}
How it's derived

The formula

D=(G−P(1+i)n) i(1+i)n−1D = \frac{\left(G - P(1+i)^n\right)\,i}{(1+i)^n - 1}

DD is the monthly deposit, GG the goal, PP what you’ve already saved, ii the monthly interest rate (annual rate ÷ 12) and nn the number of months.

Where it comes from

Your balance at the deadline has two parts.

What you have now grows by a factor of (1+i)(1+i) every month, so after nn months it becomes P(1+i)nP(1+i)^n.

The monthly deposits each grow for a different length of time. The first one grows for n−1n-1 months, the last for none. Adding them up gives a geometric series:

D[(1+i)n−1+⋯+(1+i)+1]=D (1+i)n−1iD\left[(1+i)^{n-1} + \cdots + (1+i) + 1\right] = D\,\frac{(1+i)^n - 1}{i}

Set the two parts equal to the goal and solve for DD:

P(1+i)n+D (1+i)n−1i=GP(1+i)^n + D\,\frac{(1+i)^n - 1}{i} = G

That rearranges to the formula above. With no interest, it simplifies to the obvious D=(G−P)/nD = (G - P)/n.

Worked example

Saving for $20,000 in 3 years, starting with $2,000, in an account paying 4%. So i=0.04/12i = 0.04/12 and n=36n = 36:

(1+i)36=1.1272D=(20000−2254)×0.0033330.1272=465(1+i)^{36} = 1.1272 \qquad D = \frac{(20000 - 2254)\times 0.003333}{0.1272} = 465

About $465 a month. You deposit $18,732 in total, and interest supplies the remaining $1,268.

Watch out for

  • Rates change. Savings account rates move with the economy. Recalculate every so often.
  • Investments aren’t savings. For stock market money, a steady rate is an assumption, not a promise. For a goal with a fixed deadline, it’s safer to plan with a low rate.

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