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Financial Algebra and Computations
Financial algebra, financial calculus, numerical methods, derivatives pricing, derivation of formulas and related computations.
Financial algebra is centered around the idea that money produces more of its kind by the application of compound interest.
Concepts and formulas for the pricing of financial derivatives.
Derivations and methods of financial calculus.
Compound Interest Calculator
Compound interest calculator for the growth of a one-off investment with compound interest of variable compounding frequency.
Present Value Calculator
Interest rate calculator for the present value of future income, that is, what future income is worth as of today.
Inflation Calculator
Interest rate calculator determining the loss of real purchasing power of money balances from inflation over variable time spans.
Return on Investment Calculator
Interest rate calculator for the rate of return on an investment (ROI) taking the invested amount and sales proceeds as inputs.
Savings Plan Calculator
Interest rate calculator that determines the growth of a savings plan with regular deposits and interest earnings.
Pension Present Value Calculator
Financial calculator that determines the present value of a pension or other types of long-term regular income.
Asset Valuation
Financial calculator for asset valuation based on regular income such as dividends for stocks or rents for real property.
Installment Loan Calculators
Installment loan calculators for the height of installments, underlying interest rate and end of term balance of installment loans.

Interest Rate Calculators

Interest rate calculators determine the effects of interest on account balances. This page gives an overview of our types of interest rate calculators, which serve practical as well as academic purposes.

Generally, the calculations perform valuations of interest bearing accounts. They also assess investment performance and help selecting profitable investment opportunities. Moreover, the computations are useful for drafting and verifying financial service contracts. For instance, the installment loan calculators compute loan contract details like the height of installments. As another application, the savings plan calculator projects balances for certain types of pension insurances.

In addition to valuation functions, all calculator pages include explanations on the underlying financial economics and mathematical formulas. They are therefore suitable for trying out the theoretical effects of compound interest at practical examples.

Compound Interest Calculator

The compound interest calculator outputs the exponential growth of a one-off investment with compound interest. In order to understand the compound interest effect, this calculator will be a good starting point.

Sample interest rate calculator output: exponential growth with compound interest.
Exponential growth with compound interest.

Savings Plan Calculator

The savings plan calculator accumulates wealth with compound interest, much like the simple compound interest calculator. However, in this application, savers pay regular contributions and not a one-off investment as before. As a consequence, the increase in value through contributions initially outweighs capital gains.

Savings plan interest rate calculator output with constant contributions and compound interest.
Growth of a savings plan with constant contributions and compound interest.

Present Value Calculator

The present value calculator determines the value of future income at present time. In contrast to the previous examples with exponential growth, this application of compound interest has the reverse effect of an exponential decline.

Exponential decline of the present value.
Exponential decline of the present value of future income.

Pension Present Value Calculator

The pension present value calculator determines the current value of long-term pension entitlements. It converts constant, regularly drawn payments into a one-time payment that is drawn immediately. An example application would be an option to have a pension insurance paid out as an immediately due severance payment. As indicated in the diagram below, even pensions drawn at perpetuity have finite present values. Therefore, a conversion into a one-time payment is (almost) always possible.

Pension present value interest rate calculator for the total value of pension payments.
Present value of a constant pension at 10% interest over the number of years the pension is drawn.

Inflation Calculator

The inflation calculator determines losses in purchasing power due to inflation. Results are equivalent to those of the present value computation, except that the applicable interest is not a market rate, but derived from price indices.

Devaluation of money by inflation.
Devaluation of monetary balances by inflation.

Asset Valuation Calculator

The asset valuation calculator provides a simple method of estimating fair purchase prices for investment assets. In order to find a fair price, it computes the market value for all the income that an asset generates. This calculator can help selecting profitable investment opportunities. However, when low rates of return create speculative bubbles, its valuation method may fail.

Speculative bubbles with rates of return approaching the expected growth of generated income.

Return on Investment Calculator

This interest rate calculator determines the annualized return on investment (ROI) from buying and selling assets assuming exponential growth.

Interest rate calculator for return on investment with exponential growth.
Annualized return on investment assuming exponential growth.

Installment Loan Calculators

The installment loan calculators are interest rate calculators for the drafting and verification of installment loan contracts.

Loan repayment for installment loan contracts.
Installment loan repayment depending on the height of installments.


Compound interest: Wikipedia.org

Mortgage Loans: Wikipedia.org

Amortization calculator: Wikipedia.org

Similar Computations

Interest rate calculators in German: zinseszins.de

Published: October 31, 2021
Updated: August 22, 2022

Financial Algebra
Financial Algebra