Starting capital plus ongoing savings rate

📖 The story

Tyler has already saved $12,000 and adds another $200 monthly on top. At 7 % return he wants to know the result after 20 years.

ℹ Starting capital earns interest too, ordinary installments.

Change any number and press "Calculate" – or use "Type in" on the right to watch it entered.

What you learn

Starting capital and an ongoing rate compound on each other: the existing money earns interest over the full term – combining both lifts your final result considerably.

In short: Existing starting capital earns interest over the entire term and lifts the final result considerably.

Formula

FV = K0·q^n + R·(q^n − 1)/(q − 1), q = (1+i_eff)^(1/m)

With the example numbers

q = (1+0,0700)^1/12 = 1,005654, n = 20·12 = 240
FV = 12.000,00 €·qⁿ + 200,00 €·(qⁿ−1)/(q−1) = 147.943,49 €

How to read the formula

Every installment earns interest until the end – early installments longer, late ones shorter. The bracket (qⁿ−1)/(q−1) sums up all these differently compounded contributions at once. q is the growth factor per period: from the effective rate p.a. the matching monthly factor is derived via the ¹ᐟᵐ root. Takeaway: it is not the sum of the deposits that counts, but how long each dollar is allowed to work.

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