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A savings account

If you deposit the same amount at the end of each period, and the interest stays fixed, the balance becomes a geometric series. Each deposit has had time to grow for as many periods as remain after it. Right after the last deposit, that last deposit has not yet earned interest. The formula uses the growth factor and the number of deposits. A first deposit at the start of the period is a different situation.

S=a⋅kn−1k−1S = a \cdot \frac{k^n - 1}{k - 1}right after the last deposit
k=1+rk = 1 + rgrowth factor

Symbols

aadeposit per periodNOK
rrinterest per period
nnnumber of periods

Example

10,000 NOK at the end of each year for 5 years, at 4% interest.

S=10 000⋅1.045−10.04≈54 163.2S = 10\,000 \cdot \dfrac{1.04^5 - 1}{0.04} \approx 54\,163.2 NOK.

The formula's moment is right after the last deposit.
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Part of Mathematics S2: Savings, loans and present value.