Advanced compound interest calculator with capitalization and regular contributions. Calculate savings taking into account the frequency of capitalization and additional contributions
The compound interest calculator is a professional tool for calculating savings taking into account the capitalization of interest and regular contributions. Compound interest is when interest is compounded on interest, significantly increasing your total savings amount. The calculator takes into account various capitalization frequencies (daily, weekly, monthly, quarterly, semi-annually, annually) and regular contributions to accurately predict capital growth.
Compound interest is a powerful tool for building wealth. The more often capitalization occurs (accrual of interest on interest), the greater the total amount. For example, at the same interest rate and term, daily capitalization will give more income than annual capitalization. The calculator automatically calculates the effective interest rate (EAR), which shows the real yield taking into account the frequency of capitalization.
Let's look at practical examples of calculating savings using compound interest for various scenarios:
Initial capital 100,000 ₽ at 12% per annum for 5 years, monthly capitalization
Input data:
Starting capital: 100,000 ₽
Rate: 12% per annum
Duration: 5 years
Capitalization: Monthly
Monthly fees: 0 ₽
Annual fees: 0 ₽Calculation:
Monthly rate: 12% / 12 = 1%
Periods: 5 years × 12 = 60 months
Formula: FV = PV × (1 + r)^n
FV = 100,000 × (1 + 0.01)^60
FV = 100,000 × 1.8167
Total amount: 181,670 ₽
Interest: 81,670 ₽Total amount:
Total amount: 181,670 ₽
Percentage:
Interest: 81 670 roubles
Without contributions, the initial capital increased by 1.82 times in 5 years thanks to compound interest
Initial capital 50,000 ₽, monthly contributions 10,000 ₽ at 10% per annum for 10 years, monthly capitalization
Input data:
Starting capital: 50,000 ₽
Rate: 10% per annum
Duration: 10 years
Capitalization: Monthly
Monthly fees: 10,000 ₽
Annual fees: 0 ₽Calculation:
Monthly rate: 10% / 12 = 0.833%
Periods: 10 years × 12 = 120 months
Accumulations: 50,000 × (1.00833)^120 + 10,000 × ((1.00833)^120 - 1) / 0.00833
Total amount: ~2,047,000 RUR
Total contributions: 50,000 + (10,000 × 120) = 1,250,000 ₽
Interest: ~797,000 ₽Total amount:
Total amount: ~2,047,000 RUR
Percentage:
Interest: ~797 000 roubles
Regular monthly contributions significantly increase the total amount thanks to compound interest
Initial capital 200,000 ₽ at 8% per annum for 20 years, daily capitalization
Input data:
Starting capital: 200,000 ₽
Rate: 8% per annum
Duration: 20 years
Capitalization: Daily
Monthly fees: 0 ₽
Annual fees: 0 ₽Calculation:
Daily rate: 8% / 365 = 0.0219%
Periods: 20 years × 365 = 7,300 days
FV = 200,000 × (1 + 0.08/365)^7300
FV = 200,000 × 4.9523
Total amount: 990,460 RUR
Interest: 790,460 ₽Total amount:
Total amount: 990,460 RUR
Percentage:
Interest: 790 460 roubles
Daily capitalization maximizes returns over the long term
Initial capital 500,000 ₽, annual contributions 100,000 ₽ at 7% per annum for 30 years, quarterly capitalization
Input data:
Starting capital: 500,000 ₽
Rate: 7% per annum
Duration: 30 years
Capitalization: Quarterly
Monthly fees: 0 ₽
Annual fees: 100,000 ₽Calculation:
Quarterly rate: 7% / 4 = 1.75%
Periods: 30 years × 4 = 120 quarters
Savings with annual contributions at the end of each year
Total amount: ~9,850,000 RUR
Total contributions: 500,000 + (100,000 × 30) = 3,500,000 ₽
Interest: ~6,350,000 RURTotal amount:
Total amount: ~9,850,000 RUR
Percentage:
Interest: ~6 350 000 roubles
Long-term savings with regular contributions can significantly increase capital for retirement
Initial capital 100,000 ₽ at 12% per annum for 5 years at different capitalization frequencies
Input data:
Starting capital: 100,000 ₽
Rate: 12% per annum
Duration: 5 years
Capitalization: Various options
Monthly fees: 0 ₽
Annual fees: 0 ₽Calculation:
Annually: 100,000 × (1.12)^5 = 176,234 ₽
Once every six months: 100,000 × (1.06)^10 = 179,085 ₽
Quarterly: 100,000 × (1.03)^20 = 180,611 ₽
Monthly: 100,000 × (1.01)^60 = 181,670 ₽
Daily: 100,000 × (1 + 0.12/365)^1825 = 182,206 ₽Total amount:
Difference: up to 5,972 ₽
Percentage:
Height: 82,206 ₽ (maximum)
The more often the capitalization, the greater the final amount - the difference can be significant
Initial capital 300,000 ₽, monthly contributions 5,000 ₽, annual contributions 50,000 ₽ at 9% per annum for 15 years, monthly capitalization
Input data:
Starting capital: 300,000 ₽
Rate: 9% per annum
Duration: 15 years
Capitalization: Monthly
Monthly fees: 5,000 ₽
Annual fees: 50,000 ₽Calculation:
Monthly rate: 9% / 12 = 0.75%
Periods: 15 years × 12 = 180 months
Total amount: ~3,450,000 RUR
Total contributions: 300,000 + (5,000 × 180) + (50,000 × 15) = 2,400,000 ₽
Interest: ~1,050,000 RURTotal amount:
Total amount: ~3,450,000 RUR
Percentage:
Interest: ~1,050,000 roubles
A mixed contribution strategy allows you to flexibly plan savings with maximum benefit
The calculation of compound interest involves several formulas depending on the availability of regular contributions and the frequency of capitalization.
Basic formula: FV = PV × (1 + r/n)^(n×t), where FV is future value, PV is initial capital, r is annual rate, n is capitalization periods per year, t is term in yearsWith regular contributions: FV = PV×(1+r/n)^(n×t) + PMT×(((1+r/n)^(n×t)-1)/(r/n)), where PMT is the amount of the regular contributionEffective rate: EAR = (1 + r/n)^n - 1, where r is the nominal rate, n is capitalization periodsUsing a compound interest calculator provides many benefits for savings planning.
An accurate calculation of savings helps you plan long-term financial goals: retirement, major purchases, children’s education.
A quick comparison of different capitalization frequencies and contribution amounts helps you choose the optimal savings strategy.
Understanding the impact of capitalization frequency and contribution size allows you to maximize the return on savings.
To maximize your returns using compound interest, follow our recommendations:
Compound interest is when interest is calculated not only on the initial capital, but also on the interest already accrued. This means that with each capitalization period, the amount on which interest accrues increases, resulting in exponential capital growth. Example: 100,000 ₽ at 10% per annum for the year: simple interest = 110,000 ₽, compound interest (monthly) = 110,471 ₽.
Basic formula: FV = PV × (1 + r/n)^(n×t), where FV is the total amount, PV is the initial capital, r is the annual rate in decimals (12% = 0.12), n is the number of capitalization periods per year (12 for monthly), t is the term in years. Example: 100,000 ₽, 12% per annum, monthly, 5 years: FV = 100,000 × (1 + 0.12/12)^(12×5) = 181,670 ₽.
Simple interest is accrued only on the initial capital, complex interest - on capital + accumulated interest. With simple interest: 100,000 ₽ × 10% × 5 years = 150,000 ₽. For complex (monthly): 100,000 ₽ × (1 + 10%/12)^60 = 164,531 ₽. The difference increases with time and bet size.
Interest capitalization is the process of adding accrued interest to the principal amount of the deposit, after which interest is accrued on the increased amount. The frequency of capitalization can be daily, weekly, monthly, quarterly, semi-annually or annually. The more often the capitalization, the greater the final amount.
The more frequent the capitalization, the better for the investor. Daily capitalization gives the maximum income, then weekly, monthly, etc. At the same rate and term, the difference between daily and annual capitalization can be several percent of the total amount. However, in practice, banks often offer a higher rate with less capitalization, so it is important to compare the effective rate.
The effective interest rate (EAR) shows the real yield taking into account the frequency of capitalization. Formula: EAR = (1 + r/n)^n - 1, where r is the nominal rate, n is the capitalization periods. Example: nominal rate 12%, monthly capitalization: EAR = (1 + 0.12/12)^12 - 1 = 12.68%. This means the real return is 12.68% instead of 12%.
For regular contributions, the annuity formula is used: FV = PV×(1+r)^t + PMT×(((1+r)^t-1)/r), where PMT is the contribution amount. Example: initial capital 100,000 ₽, monthly contributions 5,000 ₽, 10% per annum, 10 years: the total amount will be ~1,095,000 ₽ (of which contributions 700,000 ₽, interest ~395,000 ₽).
Depends on the amount of contributions and interest rate. Examples: Contributions 10,000 ₽/month, 8% per annum: total amount ~5,900,000 ₽ (contributions 2,400,000 ₽, interest ~3,500,000 ₽). Contributions 20,000 ₽/month, 10% per annum: total amount ~15,300,000 ₽ (contributions 4,800,000 ₽, interest ~10,500,000 ₽).
Compound interest produces higher returns by compounding interest on interest. In the short term (1-2 years) the difference is small, but in the long term (10+ years) the difference becomes significant. Example: 100,000 ₽, 10% per annum, 10 years: simple interest = 200,000 ₽, compound interest (monthly) = 270,704 ₽. The difference is 70,704 ₽ (35% more).
Use the inverse formula: PV = FV / (1 + r/n)^(n×t). Example: you need to accumulate 1,000,000 rubles in 10 years at 8% per annum with monthly capitalization: PV = 1,000,000 / (1 + 0.08/12)^(12×10) = 450,524 rubles. You need to invest 450,524 ₽ today or make monthly contributions of ~5,500 ₽.
With daily capitalization, interest is accrued 365 times a year, with annual capitalization - 1 time. This means that on the first day of the second year, you begin to earn interest on the interest accrued in the first year. At a rate of 12% and a period of 5 years: annual = 176,234 ₽, daily = 182,206 ₽. The difference is 5,972 ₽ (3.4%).
Regular contributions significantly increase the total amount, since each contribution begins to earn interest immediately. Example: 100,000 ₽, 10% per annum, 10 years without contributions = 270,704 ₽. With monthly contributions of 5,000 ₽ = 1,015,000 ₽. Contributions added RUB 744,296 to the total.
Monthly contributions are more profitable than annual ones for the same total amount, since the money starts working earlier. Example: 12,000 ₽/year (1,000 ₽/month), 10% per annum, 10 years: monthly contributions = ~207,000 ₽, once a year = ~199,000 ₽. Difference ~8,000 ₽ (4%). The higher the rate and the longer the term, the greater the difference.
Bank deposits use compound interest with a specified capitalization frequency. Use our calculator by entering the deposit amount, bank interest rate, term and frequency of capitalization (usually monthly or quarterly). The calculator will show the total amount accurate to the penny.
The nominal rate is the rate quoted by the bank (for example, 12% per annum). Effective rate (EAR) - real return taking into account capitalization. With a nominal 12% and monthly capitalization, the effective rate = 12.68%. The effective rate is always higher than the nominal rate when capitalization is more than once a year.
Compound interest also works for investments (stocks, bonds, mutual funds). Use the calculator, indicating the initial capital, the average expected return (instead of the interest rate), the investment period and periodic replenishments (if you plan). Important: return on investment is not guaranteed, unlike a bank deposit.
Compound interest also applies to loans—banks charge interest on interest on late payments or on certain types of loans. However, for ordinary consumer loans and mortgages, annuity or differentiated payments are used, where compound interest is taken into account in the formula, but the payment scheme is different.
Most banks capitalize interest on a monthly or quarterly basis. Daily capitalization is less common, but provides maximum profitability. When choosing a deposit, compare not only the interest rate, but also the frequency of capitalization, using the effective rate for comparison.
The Rule of 72 is a quick way to determine how many years it will take for your capital to double: 72 / interest rate = years until doubling. Example: at 12% per annum: 72 / 12 = 6 years (more precisely 6.12 years). This rule works quite accurately for rates from 6% to 10%. For a more accurate calculation, use a calculator.
If the rate changes, the calculation is divided into periods with different rates. Example: 100,000 ₽, first 3 years at 10%, next 2 years at 12%: FV = 100,000 × (1.10)^3 × (1.12)^2 = 168,948 ₽. For such complex calculations, it is better to use a calculator with the ability to specify different rates by period.
The absolute amount of interest depends on the initial capital (more capital = more interest), but the relative return (percentage of growth) is the same. Example: 100,000 ₽ and 1,000,000 ₽ at 10% per annum, 10 years: the first will grow to 270,704 ₽ (an increase of 170.7%), the second to 2,707,041 ₽ (an increase of 170.7%). The growth percentage is the same.
For retirement, use a long term (20-30 years) with regular contributions. Example: initial capital 500,000 ₽, monthly contributions 10,000 ₽, 7% per annum, 25 years: total amount ~9,200,000 ₽ (contributions 3,500,000 ₽, interest ~5,700,000 ₽). Start saving as early as possible - time is on your side.
Compound interest is always more profitable than simple interest at the same rate and term. The difference increases over time. For 1 year at 10%: the difference is small (~0.5%). For 10 years: the difference is significant (~35-40%). For 30 years: the difference is huge (more than 2 times). Always choose deposits and investments with compound interest.
Use the formula: t = ln(3) / (n × ln(1 + r/n)), where n are capitalization periods. For a quick estimate: at 12% per annum, the capital will triple in about 9.6 years (monthly capitalization). At 8% per annum - for ~14 years. The higher the bet, the faster the tripling.
Yes, the tax reduces the total amount. For deposits over 1 million rubles and a rate higher than the key rate of the Central Bank + 5%, a tax of 13% is levied on income. Example: deposit 2,000,000 ₽, income 300,000 ₽, tax ~39,000 ₽, total 260,000 ₽ net profit. Consider taxes when planning your savings.
Bonds often pay coupons (interest) regularly, which can be reinvested at the same rate. Use the compound interest formula with periodic payments. Example: bond 100,000 ₽, coupon 8% per annum (4% every six months), reinvestment at 8%, 5 years: total amount ~148,024 ₽.
Mortgage payments are calculated using an annuity formula that already takes into account compound interest. Monthly payment = Amount × (r × (1+r)^n) / ((1+r)^n - 1), where r is the monthly rate, n is the number of months. This is compound interest in action - each payment reduces the debt on which interest is charged.
Real yield = Nominal yield - Inflation. Example: deposit 10% per annum, inflation 6%: real return = 4%. Use the real rate in the formula: FV = PV × (1 + (r - inflation)/n)^(n×t). When inflation is higher than the rate, capital loses purchasing power, despite growth in rubles.
The more frequent the contributions for the same total amount, the better. Weekly contributions are better than monthly ones, monthly ones are better than annual ones. Example: 12,000 ₽/year, 10% per annum, 10 years: annually = ~199,000 ₽, monthly (1,000 ₽) = ~207,000 ₽, weekly (~231 ₽) = ~207,500 ₽. But convenience is also important - find a balance.
For partial withdrawals, the calculation is divided into periods before and after withdrawal. Example: 100,000 ₽, 10% per annum, after 3 years 30,000 ₽ were withdrawn, continue for another 2 years: FV1 = 100,000 × (1.10)^3 = 133,100 ₽, after withdrawal: 103,100 ₽, FV2 = 103,100 × (1.10)^2 = 124,751 ₽. Each withdrawal reduces the future amount.
APR (Annual Percentage Rate) - nominal annual rate excluding capitalization. APY (Annual Percentage Yield) is an effective rate taking into account capitalization (analogous to EAR). Example: APR = 12%, monthly capitalization: APY = 12.68%. Always compare APY, not APR, when choosing investments.
For cryptocurrencies, use the average expected return instead of the interest rate. Important: cryptocurrencies are very volatile, profitability is not guaranteed. The formula is the same: FV = PV × (1 + profitability)^t. Example: initial amount 100,000 ₽, average yield 20% per annum, 5 years: FV = 248,832 ₽. But actual returns may vary greatly.
Yes, use the BS function (FV): =BS(rate/periods, periods×years, -payment, -initial_amount). Example: =BS(12%/12; 12*5; -5000; -100000) for 100,000 ₽, monthly installments 5,000 ₽, 12% per annum, 5 years. Or use our online calculator for convenience.
Term has an exponential impact thanks to compound interest. Each additional year increases the total not linearly, but exponentially. Example: 100,000 ₽, 10% per annum: 5 years = 164,531 ₽, 10 years = 270,704 ₽ (not 2 times more, but 1.65 times thanks to compound interest), 20 years = 732,807 ₽ (4.45 times more than 5 years).
The calculation is divided into periods with different contribution amounts. Example: for the first 3 years, contributions are 5,000 ₽/month, the next 2 years are 10,000 ₽/month: calculated separately for each period, taking into account the accumulated amount of the previous period. For an accurate calculation, use a calculator or financial calculator.
Continuous compounding is a mathematical limit for an infinite capitalization rate. Formula: FV = PV × e^(r×t), where e = 2.71828 (Euler number). Example: 100,000 ₽, 10% per annum, 5 years: FV = 100,000 × e^(0.10×5) = 164,872 ₽. In practice, banks use discrete capitalization (daily, monthly), which is close to continuous.
Savings accounts often have monthly capitalization. Use the calculator, indicating the amount in the account, the bank's interest rate, capitalization frequency (usually monthly) and planned replenishments. Example: initial balance 50,000 ₽, top-up 10,000 ₽/month, 6% per annum, 5 years: total amount ~730,000 ₽.
Yes, early closing usually reduces the interest rate (down to the call rate, usually 0.01-0.1% per annum). The calculation is carried out until closing at the full rate, then at a reduced rate or without interest at all, depending on the terms of the deposit. Always read the terms of the contract before closing early.