📖 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.
Topics › Saving & Compound Interest › Starting capital plus ongoing savings rate
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Saving & Compound Interest
Starting capital plus ongoing savings rate
Change any number and press "Calculate" – or use "Type in" on the right to watch it entered step by step.
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 $
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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