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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.
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.

Savings Plan Calculator

The savings plan calculator determines the growth of a savings account with regular deposits and interest earnings. Results are applicable to certain types of pension insurances with fixed interest and contributions. Usage instructions and explanations annuity savings plans follow after the calculation form.

Usage Instructions for the Savings Plan Calculator

Please fill the calculator form with the height of regular deposits, a nominal interest rate, and the duration of the savings plan in years. All fields above the calculate button refer to input values, which you can change to your needs. From these inputs the form computes the final account balance and total capital gains.

Per default, the computation assumes monthly contributions. Most users will be fine with this setting. However, you may choose four (quarterly), two (semi-annual), or one (annual) contributions.

In addition to the final balance, the calculator produces intermediate results in its details section. Since this list can grow quite long, you may prefer to hide it by clicking on the “hide -” label in its upper right corner.

Annuity Savings Plans

Annuities are series of payments made at regular intervals and the special case of fixed payments is a fixed annuity. The future value of a fixed annuity is then a technical term for the balances output by the savings plan form. Provided that balances earn interest, their present and future values differ and the purpose of the savings plan calculation is to find out by how much.

Account balance of savings plan with totals of interest and contributions.
Account balance and totals of interest and contributions for a savings plan with $100 monthly contributions, 5% interest and 30 years duration.

At start, the growth from interest is negligible compared to contributions. Only after a sufficient balance builds in the account, interest earnings top contributions. Take the plan in the above graph as an example. With 5% of interest, savers wait more than 25 years until interest earnings match contributions. This is where the dashed blue and solid green lines cross.

To summarize, the compound interest effect lifts up annuity savings balances with considerable delay. Nevertheless, it is not necessarily a good idea to commit early to annuity savings for retirement income. Only if the interest rate exceeds inflation, savers benefit in terms of real purchasing power. However, for multiple decade savings plans it is likely that periods of high inflation cancel out interest gains.

As a consequence, savers may be better off investing in inflation protected assets, such as real property.

For better intuition on the effects of inflation, you could try out the inflation or pension present value calculators.

Mathematical Formula for the Savings Plan

The savings plan calculator uses the following mathematical formula:

FV = C0 * m / r * ((1+r/m)m*t - 1)

FV: future value of annuity savings
C0: constant contribution
r: interest rate
m: number of contributions per year
t: time in years

References

Annuities: Wikipedia.org

Similar Computations

Savings Plan Calculator in German: zinseszins.de


Published: November 1, 2021
Updated: August 20, 2022

Mathematical Economics
Economics, Statistics and Calculators