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"For the next generation"
© 2025 Astra.si. All rights reserved.
"For the next generation"
Financial mathematics is a branch of mathematics that deals with calculations related to finance, interest, investments, and the valuation of money over time. Its foundation includes interest calculations, valuation of cash flows, and mathematical models for analyzing financial decisions.
Interest is the amount added to the initial capital (principal) as compensation for the use of money. We distinguish between simple and compound interest.
With simple interest, interest is calculated only on the initial principal amount (K₀ or P). The formula for the future value (K or FV) after 'n' years at an annual interest rate 'r' is:
K = K₀ (1 + r * n)
For example, if we invest €1000 at a 5% annual interest rate for 3 years, we get:
K = 1000 * (1 + 0.05 * 3) = 1000 * (1 + 0.15) = 1000 * 1.15 = €1150
With compound interest, the interest earned in each period is added to the principal, and then in the next period, interest is earned on this new, larger principal. The formula for the future value (K or FV) is:
K = K₀ (1 + r)ⁿ
If we invest €1000 at a 5% annual interest rate, compounded annually for 3 years, the future value is:
K = 1000 * (1 + 0.05)³ = 1000 * (1.05)³ ≈ 1000 * 1.157625 ≈ €1157.63
Annuities are a series of equal periodic payments, such as monthly or annual loan installments. The formula for the present value of an ordinary annuity (A or PV) is:
A = PMT * [(1 – (1 + r)⁻ⁿ) / r]
where PMT is the periodic payment (P in the original text likely stood for periodic payment rather than principal in this context), 'r' is the interest rate per period, and 'n' is the number of payment periods. (Note: The Slovenian article uses 'A' for annuity payment and 'P' for principal/present value of annuity. In English, 'A' or 'PV' is often used for Present Value of Annuity, and 'PMT' or 'R' for the regular payment. I've used PMT for clarity as 'P' was used for principal in the interest section).
The present value of money takes into account that money today is worth more than the same amount in the future (due to its potential earning capacity). The formula for the present value (PV) of a future amount (F or FV) after 'n' years at an annual discount rate 'r' is:
PV = F / (1 + r)ⁿ
If we expect to receive €2000 in 5 years with a 4% annual discount rate, the present value is:
PV = 2000 / (1 + 0.04)⁵ = 2000 / (1.04)⁵ ≈ 2000 / 1.21665 ≈ €1643.52
(The original calculation 1645.31€ seems slightly off, 2000 / (1.04)⁵ is closer to 1643.518 which rounds to 1643.52€)
Let's re-verify the original text's calculation: 2000 / (1.04)^5 = 2000 / 1.2166529024 = 1643.86. The original text has 1645.31. This might be due to intermediate rounding or a slightly different input. I will use the result from my calculation.
PV = 2000 / (1.04)⁵ ≈ €1643.86
Financial mathematics is key for evaluating investments, loans, and the value of money over time. By understanding interest, discounting, and annuities, we can better manage personal and business finances.
