How this differs from CastroTools' other calculators
The Investment and Compound Savings calculators are built for everyday practical situations, always assuming compound interest and recurring contributions. This calculator works with the more general, textbook time-value-of-money formulas: a direct comparison between simple and compound interest, the distinction between ordinary annuities and annuities due, and present value (discounting), which is the reverse process of projecting a future value.
Formulas used
Future value with simple interest: FV = PV × (1 + rate × years)
Future value with compound interest: FV = PV × (1 + rate)^years
Future value of an ordinary annuity: FV = payment × (((1 + i)^n − 1) ÷ i)
Future value of an annuity due: FV (due) = FV (ordinary) × (1 + i)
Present value (discounting): PV = FV ÷ (1 + rate)^years
Where PV is present value, FV is future value, i is the interest rate per period, and n is the number of periods.
Practical example: simple vs compound interest
$10,000 at 8% a year over 5 years grows to $14,000 with simple interest, but to roughly $14,693 with compound interest — a difference of about $693. Over longer periods this gap widens rapidly, because compound interest starts earning interest on its own accumulated interest, while simple interest keeps earning only on the original amount.
Practical example: ordinary annuity vs annuity due
A series of 10 payments of $1,000, at a 6% rate per period, produces a future value of roughly $13,181 under the ordinary model (payment at the end of each period), and about $13,972 under the due model (payment at the start of each period) — a difference of roughly $791, resulting from each payment earning interest for one extra period under the annuity due.
Practical example: present value needed
To have $50,000 in 8 years, at a 7% annual rate, you'd need to invest roughly $29,103 today, as a single lump sum, with no additional contributions along the way. That's the present value which, compounded at the stated rate over the given period, arrives exactly at the target future value.
When to use each of these formulas
Comparing simple and compound interest helps with understanding contracts or products that still use the simple-interest convention, which is rarer today but does show up in some very short-term instruments. The ordinary annuity vs. annuity due distinction matters for lease contracts, insurance, and some retirement plans, where the payment timing (start or end of the period) changes the final result. Present value calculations are useful whenever you already know what you'll need in the future and want to check whether a lump sum available today, invested at once, would be enough.
What this calculator doesn't account for
These calculations assume a constant interest rate for the entire period and don't include taxes on earnings, account fees, or the possibility of additional contributions over time (for that, see the Investment Calculator). Use the results as a conceptual and planning reference.