How is an increase in value calculated?

Add the percentage to one as a decimal number. Raise this result to the power of the number of periods and multiply it by the starting value. For example, if a quantity increases by 5.4 percent per year for 10 years, you would multiply $1,000 by 1.054 raised to the 10th power, which is about $1,692.

Can this calculator be used to find out what interest rate is required to reach a target?

Yes. If you leave the interest rate fields blank and instead input starting value, number of years, and ending value, then the tool will calculate what annual interest rate is required to achieve that goal.

What is the difference between nominal growth and real growth?

The nominal gain is the original increase in the asset's value. The real gain takes inflation into account so you can see how your purchasing power has actually changed. Turn on the inflation option to show the value in today's money.

Can this be used to calculate depreciation?

Yes. The same formula is used to calculate depreciation but the interest rate is less than zero. Enter a negative growth rate. For example if a car has a negative growth rate of 15 percent then this tool will calculate its depreciated value.

Do results change based on how often interest is compounded?

It can change. While the compound interest calculator uses annual calculations by default, a higher frequency will result in faster growth so that the final value may be slightly higher with the same rate of return. The effective annual rate shown in the results reflects this difference.

Appreciation Calculator

Your asset

Starting value

Appreciation rate

Number of years

Final value

How often it compounds

Dropdown list for Compounding Frequency

Adjust for inflation

Show the final value in today's money.

Apply tax on the gain

Estimate what you keep after capital gains tax on the profit.

Show a rate sensitivity band

See a lower and higher estimate around your appreciation rate.

Fill in any three of starting value, appreciation rate, years, and final value. The calculator solves for the one you leave blank.

Please input values into the fields

Charts and schedule

The value growth calculator allows you to estimate the future value of an investment after a period of time. By entering the initial amount, rate of growth and length of time, the final amount is calculated using compound interest. It also supports reverse calculations: if one of the four fields are left blank, that value will be calculated. For example, it can calculate the required rate of growth to reach a target house price or how many years it would take to reach the target price.

What does value increase mean?

Appreciation refers to the increase in value of an investment over time. The rate of appreciation is the percentage that indicates the increase from the original value. It is similar to compound interest as each period the value increases by this percentage and the increased value continues to grow in the next period. The longer the length of time invested, the faster the total value grows.

Depreciation is the opposite - a decrease in value. Both are described by the same formula. A positive interest rate represents appreciation; a negative interest rate represents depreciation. For example, if a car's value decreases by 15 percent annually, this corresponds to a negative interest rate of 15 percent.

How is the increase in value calculated?

The ending value of an investment that increases in value follows the compound interest formula.

\text{finVal} = \text{stVal} \times (1 + \text{apRate})^{\text{period}}

In this formula, stVal is the starting value, apRate is the growth rate per period expressed as a decimal number and period is the number of periods. Suppose you buy a house for $150,000 and real estate in that area grows by about 5.4 percent annually. After four years it would be:

\text{finVal} = 150{,}000 \times (1 + 0.054)^{4} \approx 185{,}120.15

So the value of this house is about $185,120. The profit would be $35,120 and the total increase over four years is about 23.4 percent.

Calculating required growth rate

This tool can also work in reverse. Say you want to sell a house for $200,000 in four years that is currently worth $150,000 and you want to know what annual growth rate would be required to achieve this goal. By rearranging the formula, we can solve for the required growth rate.

\text{apRate} = \left(\frac{\text{finVal}}{\text{stVal}}\right)^{\frac{1}{\text{period}}} - 1

\text{apRate} = \left(\frac{200{,}000}{150{,}000}\right)^{\frac{1}{4}} - 1 \approx 0.07457

This is equivalent to approximately 7.457 percent per year. To use the reverse calculation mode, leave the field for growth rate blank and enter values into the other three fields. The calculator will then calculate the value.

List of input fields

The table below shows the individual input parameters and example values for a residential property.

Symbol	Meaning	Example
stVal	Starting value	150,000
apRate	Appreciation rate per year	5.4 percent
period	Number of years	4
finVal	Final value	185,120.15

Nominal and real values

Just rising numbers do not give a complete picture of the situation. Even if an asset rises 5% per year, the increase in purchasing power will be significantly less than what surface level figures suggest when prices rise by 3% annually. By activating the inflation option you can see the ending value in today's currency. This option divides the future balance by the price escalation factor. Over longer time periods this real value is more important than the nominal value.

Interest rate calculator application areas

The compound interest calculator can be used for many assets. Real estate is the most typical example and it can be used to estimate future value, gains and returns of homes to land over a holding period. Investors can use it to predict growth in stocks, bonds and funds based on expected rates of return. Collectors can use it to estimate the value of art, wine, watches or other items that increase in value due to rarity or age.

As each plan ultimately leads to a single end value, you can compare different options with varying interest rates and terms side by side.

Tips for making predictions more realistic:

Use realistic interest rates and avoid the most optimistic scenarios. Historical averages are a good reference point. In the US real estate has risen in moderate single digits percent over long periods of time, while broad stock indexes have averaged annual returns of about 7 to 10 percent before inflation. The frequency of compounding should reflect your understanding of the asset. Most calculations will be fine with an annual frequency. If the period is longer, turn on the inflation option and remember that taxes and selling costs reduce the amount actually available.

This calculator is for educational and planning purposes only and does not constitute financial advice. Gains are not guaranteed and actual results may vary depending on market conditions, the condition of the asset, and timing. Please consult a qualified professional before making any investment decisions.

Frequently asked questions

How is an increase in value calculated?: Add the percentage to one as a decimal number. Raise this result to the power of the number of periods and multiply it by the starting value. For example, if a quantity increases by 5.4 percent per year for 10 years, you would multiply $1,000 by 1.054 raised to the 10th power, which is about $1,692.
Can this calculator be used to find out what interest rate is required to reach a target?: Yes. If you leave the interest rate fields blank and instead input starting value, number of years, and ending value, then the tool will calculate what annual interest rate is required to achieve that goal.
What is the difference between nominal growth and real growth?: The nominal gain is the original increase in the asset's value. The real gain takes inflation into account so you can see how your purchasing power has actually changed. Turn on the inflation option to show the value in today's money.
Can this be used to calculate depreciation?: Yes. The same formula is used to calculate depreciation but the interest rate is less than zero. Enter a negative growth rate. For example if a car has a negative growth rate of 15 percent then this tool will calculate its depreciated value.
Do results change based on how often interest is compounded?: It can change. While the compound interest calculator uses annual calculations by default, a higher frequency will result in faster growth so that the final value may be slightly higher with the same rate of return. The effective annual rate shown in the results reflects this difference.

Related calculators

Future Value CalculatorProject the future value of an investment with compound interest, regular deposits or withdrawals, inflation adjustment, tax on gains, and reverse solving.

CAGR CalculatorCalculate the compound annual growth rate (CAGR) of an investment, or solve for the starting value, ending value, or number of years. Includes total return, doubling time, a benchmark comparison, a growth chart, and a year-by-year table.

Inflation CalculatorSee how inflation changes the value of money. Convert an amount between two years with real U.S. CPI data, or project it forward and back at a rate you choose.

CAGR CalculatorWork out a compound annual growth rate over a period entered as years, months and days or as two exact dates. Solves for the rate, the ending value, the starting value or the time required, and shows compounding against a simple average.

ROA CalculatorCalculate return on assets, net income, or total assets from any two values, with a DuPont margin-and-turnover breakdown, return on equity and leverage, average total assets, and an industry benchmark.

Capital Gains Tax CalculatorEstimate capital gains tax on a sale in any country: an automatic US federal bracket engine (0/15/20% long-term, NIIT) or a flat-rate mode with optional exclusion, inclusion-rate, long-term-discount, and surcharge levers.

Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Investopedia: Appreciation
Definition of appreciation, how it differs from depreciation, and worked examples.
Investor.gov: Compound Interest Calculator and Saving Basics
U.S. SEC explainer on compound growth, the engine behind appreciation.
Brigham & Ehrhardt, Financial Management: Theory and Practice (2016)
Standard corporate-finance text on the time value of money and future value.