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Compound Interest Calculator: Growth and Monthly Savings

Calculate compound interest with monthly contributions. Explore future savings, the rule of 72, annuity formulas, and inflation-adjusted real returns.

Bileşik Faiz & Düzenli Tasarruf Simülatörü

Zamanın ve bileşik getirinin gücüyle birikimlerinizin gelecekteki büyümesini simüle edin

₺
₺
%30
%
10 Yıl (120 Ay)
1 Yıl10 Yıl20 Yıl30 Yıl40 Yıl
Toplam Gelecek Değer
4.639.537 ₺

10 yıl sonundaki toplam net birikiminiz

Yatırılan Toplam Para
650.000 ₺

Cebinizden çıkan net anapara toplamı

Toplam Bileşik Getiri
+3.989.537 ₺

Bileşik faiz ve büyümeden elde edilen kazanç

Büyüme Çarpanı
7.14x

Paranız anaparanızın 7.1 katına ulaştı

Yatırılan Anapara (%14)Bileşik Faiz Getirisi (%86)

Yıllara Göre Portföy Büyümesi

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Compound Interest Guide: Future Value, Regular Savings, and the Snowball Effect

As the famous saying attributed to Albert Einstein goes: "Compound interest is the eighth wonder of the world; those who understand it earn it, and those who do not pay it."
With simple interest, returns are calculated only on the initial principal each period, and earnings follow a straight line (linear). With compound interest (compound returns) the interest earned each period is added to the principal; in later periods, interest itself starts earning interest. As time passes, the savings curve steepens, creating the effect known in finance as the snowball effect through exponential (exponential) growth.
HesapYap Compound Interest Calculator; simulates your estimated future portfolio value and real earnings in seconds using your initial capital, periodic return rate, investment term, and regular monthly contributions.

1. How Is Compound Interest Calculated?

The future value of a one-time initial principal with no additional deposits is calculated with this formula:

FV=P(1+rm)m×t\text{FV} = P \left(1 + \frac{r}{m}\right)^{m \times t}


  • 
    FV\text{FV}
    
    (Future Value): Estimated total savings at the end of the term.
  • 
    PP
    
    (Principal): Initial principal.
  • 
    rr
    
    : Annual nominal return rate (as a decimal: 0.30 for 30%).
  • 
    mm
    
    : Compounding frequency per year (12 for monthly, 4 for every 3 months, 1 for annually).
  • 
    tt
    
    : Total investment duration in years.

Example Simulation: TRY 50,000 Over 10 Years

Suppose you initially invest TRY 50,000 , with annual nominal interest of 30% compounded monthly (
m=12m=12

, 2.5% per month):
  • The total portfolio after 10 years (120 months) is approximately TRY 965,000 .
  • After subtracting the initial TRY 50,000, the net nominal profit earned on the principal is TRY 915,000 .

2. Saving with Regular Monthly Contributions (Future Value of an Annuity)

Making regular monthly additions instead of relying only on a one-time principal accelerates the snowball effect.
The combined formula for initial capital and regular contributions added at the end of each month:

FV=P(1+i)N+C[(1+i)N−1i]\text{FV} = P(1 + i)^N + C \left[ \frac{(1 + i)^N - 1}{i} \right]


  • 
    CC
    
    : The regular savings amount added each month.
  • 
    ii
    
    : Monthly periodic interest/return rate (
    r/12r / 12
    
    ).
  • 
    NN
    
    : Total number of months (
    t×12t \times 12
    
    ).

Example: TRY 50,000 Initially + TRY 5,000 Each Month for 10 Years

Assuming a monthly return of 2.5% (
r=%30r=\%30

):
  • Total Principal Paid Out of Pocket:
    50.000+(5.000×120)=650.000 TL50.000 + (5.000 \times 120) = \mathbf{650.000\text{ TL}}
    
    
  • Total Savings at the End of Year 10: approximately TRY 5,400,000
Compared with the TRY 650,000 invested, the substantial surplus of approximately TRY 4.75 million clearly shows the exponential power of compound interest over time.

3. Key Differences Between Simple and Compound Interest

Criterion
Simple Interest
Compound Interest
Return Base
Calculated only on the initial principal
Calculated on principal + accumulated past interest each period
Growth Pattern
Straight-Line (Linear): Earns the same fixed amount each year
Exponential (Exponential): Growth accelerates over the years
Reinvestment of Earnings
Interest is withdrawn; principal remains fixed
Interest is added to savings and reinvested
Long-Term Outcome
Falls behind compound interest over time
Grows the portfolio geometrically over time

4. Rule of 72: How Many Years Until Your Savings Double?

In finance, the time needed for an investment to double at a fixed return rate can be estimated mentally using the Rule of 72 :

I˙kiye Katlanma Su¨resi (Yıl)≈72Yıllık Getiri Oranı (%)\text{İkiye Katlanma Süresi (Yıl)} \approx \frac{72}{\text{Yıllık Getiri Oranı (\%)}}


  • 12% Annual Return:
    72/12=6 Yılda72 / 12 = \mathbf{6\text{ Yılda}}
    
    to double.
  • 24% Annual Return:
    72/24=3 Yılda72 / 24 = \mathbf{3\text{ Yılda}}
    
    to double.
  • 36% Annual Return:
    72/36=2 Yılda72 / 36 = \mathbf{2\text{ Yılda}}
    
    to double.

5. Inflation and the Fisher Real Return Equation

Nominal growth in money does not mean purchasing power rises at the same rate. To see whether your savings create real wealth, you need to adjust for inflation:

rreel=1+rnominal1+π−1r_{\text{reel}} = \frac{1 + r_{\text{nominal}}}{1 + \pi} - 1


(Here,
π\pi

represents the inflation rate for the same period).
Example: If an investment provides an annual 40% nominal return while inflation over the same period is 35% :
rreel=1,401,35−1≈%3,70r_{\text{reel}} = \frac{1{,}40}{1{,}35} - 1 \approx \mathbf{\%3{,}70}

Although your nominal gain appears to be 40%, the net increase in your real purchasing power is only 3.7%.

6. Remember Withholding (Income Tax) Deductions

In Türkiye, returns from time deposits, investment funds, or bonds are subject to deductions under the Gelir Vergisi Kanunu (Income Tax Law, Provisional Article 67), known as withholding tax at source . To determine how much of the calculator's gross return you actually keep, the withholding rate for the investment (for example, 5%, 7.5%, or 10%) must be deducted from earnings.

Frequently Asked Questions

What is the most important factor in compound returns? By far the most important factor is time. Starting regular savings with a small amount at a young age mathematically builds much greater wealth than starting with larger amounts later in life.
What is the difference between compound interest and compound returns? Compound interest refers only to adding interest payments from deposits and debt securities. Compound returns are the broader concept of growth across investment types when stock dividends or fund earnings are reinvested.
Does every investment provide compound returns? If you immediately put interest, profit shares, or dividends back into the same investment instead of spending them (reinvestment / reinvestment), that instrument generates compound returns for you. If you withdraw earnings, the return becomes simple interest.

Sources and Further Reading

  • CFA Institute – Time Value of Money & Compound Interest Curriculum.
Financial Information and Disclaimer: Calculations and simulations on this page are provided for general mathematical education and planning; they are not a guarantee of earnings or personalized investment advice. Withholding taxes, transaction commissions, fund management fees, and market risks must be considered when making investment decisions.