How this calculator works
A continuous nominal rate is an annual force of interest: growth occurs exponentially rather than at discrete interest-credit dates. Contributions remain discrete and may be made at interval starts or completed interval ends. You can instead supply an effective annual return, or solve the force of interest needed for a target. Tables show growth on both the initial balance and contributions. The opening row includes the first beginning deposit when the horizon is positive; later exact-boundary rows show the closing balance before the next beginning deposit.
Formula
F_initial = P exp(rt). Each deposit C_j contributes C_j exp(r(t-t_j)). Effective annual return = exp(r)-1; real final value = nominal final value/(1+inflation)^t.
Worked example
At a continuous annual rate ln(1.1), an initial $1,000 becomes $1,210 after two years. Adding $100 at each year end brings the balance to $1,420; at a zero rate, the same principal and two deposits total $1,200.
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Frequently asked questions
Is a 5% continuous rate the same as a 5% effective rate?
No. A 5% continuous quote has an effective annual rate of exp(0.05)-1, approximately 5.1271%.
Are contributions continuous too?
No. They occur at the selected discrete frequency. A continuously flowing payment stream requires an integral rather than these individual deposits.
Can I separate the sources of growth?
Yes. Outputs show growth on the opening balance and on contributions, as well as the total invested capital.