Input data

Initial capital
Annual inflation (expected)	%
Expected rate of return	%
Years to predict

Forecasted capital value

Real value of your capital after 10 years will be 1248.86.
It is 28.01% more than today's value.

Capital worth in time - simulation

Year	Capital value	Investment interest	Value decrease due to inflation	Relative value change to the initial amount [%]
0	1000.00	50.00	25.00	0.00
1	1025.00	51.25	25.63	2.50
2	1050.63	52.53	26.27	5.06
3	1076.89	53.84	26.92	7.69
4	1103.81	55.19	27.60	10.38
5	1131.41	56.57	28.29	13.14
6	1159.69	57.98	28.99	15.97
7	1188.69	59.43	29.72	18.87
8	1218.40	60.92	30.46	21.84
9	1248.86	62.44	31.22	24.89
10	1280.08	64.00	32.00	28.01

Some facts

I. Let's assume, we put 1000$ into bank deposit with 5% interest rate. After first year, we get 50$ interests, so our total capital become 1050$. Let's say, that we put total amount (it means 1050$) to the same deposit next year. Interest rate is still 5%, but base to compute interest value is 1050$ (instead of 1000$ in first year).
Let's try to summarize:
- First year: we put 1000$, get 50$ of interests (5% from 1000$)
- Second year: we put 1050$, get 52.50$ of interests (5.25% from 1000$)
- Third year: we put 1102.5$, get 55.125$ of interests (5.51% from 1000$)
- etc...
It turned out, that our effective interests (it means computed relative to initial 1000$) increase from year to year. This phenomena is known as compound interest or colloquially and more general snow ball effect.
We can generalize above steps to create simple formula for capital worth after n years:

$V = V_0 \times (1 + r)^n$

where:
- V = capital after n years,
- $V_0$ = start capital at begin of first year,
- r = annual interest rate,
- n = how many years have passed.
Unfortunately, the same mechanism can also work against us. If we repeat calculations done above, but assumming, that we lose instead of earning ("negative interest rate"), then it turned out that we lose more and more each year.
Some form of money loss is inflation. Let's say, we put our money under the carpet (instead of bank deposit in first example). What is going on with our money? It's true that amount doesn't change in time - 100$ bill will be still the same 100$ bill after few years. However - it turned out - that it's real value can be smaller in future. The reason of this is price growth. If prices are going up, we can buy less for the same money, so our money are effectively worth less. It's so called decline in purchasing power of money - or simply speaking - inflation.
We can modify previous formula to take into acount inflation. Then we get below formula:

$V = V_0 \times (1 + \frac{r - i}{1 + i})^n$

where:
- V = capital after n years,
- $V_0$ = start capital at begin of first year,
- r = annual interest rate,
- i = annual inflation rate,
- n = how many years have passed.
From the above formula it can be seen that if inflation exceeds the annual interest rate (i> r), then we will be losing more and more every year.

How to use this tool

Simply fill the form below and calculla will simulate real value of your money in next years.

Initial capital - it is amount of money used as base for calculations. Calculla will show you how real worth of this amount will be changing in future.
Inflation - it is expected inflation rate for next years. If you want simply show result of investments without including inflation, then you can set this field to zero.
Rate of interest - it is average investment income expected in next years. If you set this field to zero, then you'll see what's gonna happen when you put your money "under the mattress".
Years to predict - time range to simulate (in years). For example, if you want to check real worth of your money after ten years, set this field to 10.

Tags and links to this website

Tags:

compound_interest · compound_inflation · compound_rate_of_return · real_worth_of_money · money_worth · money_worth_forecast

Tags to Polish version:

procent_skladany · skumulowana_inflacja · skumulowana_stopa_zwrotu · wartosc_pieniadza · wartosc_pieniadza_prognozowanie · przyszla_wartosc_pieniadza · kalkulator_procentu_skladanego

Permalink

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http://calculla.com/compound_interest?inInitialCapital=1000&inInflationRate=2.5&inYearlyReturnRate=5&inYearsToPredict=10

Links to external sites (leaving Calculla?)

Ancient version of this site - links

"Calculla v1" version of this calculatorIn December 2016 the Calculla website has been republished using new technologies and all calculators have been rewritten. Old version of the Calculla is still available through this link: v1.calculla.com. We left the version 1 of Calculla untouched for archival purposes.
Direct link to the old version:

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