## Calculator Use

The compound interest calculator lets you see how your money can grow using interest compounding.

Calculate compound interest on an investment, 401K or savings account with annual, quarterly, daily or continuous compounding.

We provide answers to your compound interest calculations and show you the steps to find the answer. You can also experiment with the calculator to see how different interest rates or loan lengths can affect how much you'll pay in compounded interest on a loan.

Read further below for additional compound interest formulas to find principal, interest rates or final investment value. We also show you how to calculate continuous compounding with the formula A = Pe^rt.

## The Compound Interest Formula

This calculator uses the compound interest formula to find principal plus interest. It uses this same formula to solve for principal, rate or time given the other known values. You can also use this formula to set up a compound interest calculator in Excel^{®1}.

**A = P(1 + r/n) ^{nt}**

In the formula

- A = Accrued amount (principal + interest)
- P = Principal amount
- r = Annual nominal interest rate as a decimal
- R = Annual nominal interest rate as a percent
- r = R/100
- n = number of compounding periods per unit of time
- t = time in decimal years; e.g., 6 months is calculated as 0.5 years. Divide your partial year number of months by 12 to get the decimal years.
- I = Interest amount
- ln = natural logarithm, used in formulas below

### Compound Interest Formulas Used in This Calculator

The basic compound interest formula A = P(1 + r/n)^{nt} can be used to find any of the other variables. The tables below show the compound interest formula rewritten so the unknown variable is isolated on the left side of the equation.

Compound Interest Formulas

Calculation

Formula

Calculate accrued amount

Principal + Interest

A = P(1 + r/n)^{nt}

Calculate principal amount

Solve for P in terms of A

P = A / (1 + r/n)^{nt}

Calculate principal amount

Solve for P in terms of I

P = I / ((1 + r/n)^{nt} - 1)

Calculate rate of interest

As a decimal

r = n((A/P)^{1/nt} - 1)

Calculate rate of interest

As a percent

R = r * 100

Calculate time

Solve for t

ln is the natural logarithm

t = ln(A/P) / n(ln(1 + r/n)), then also

t = (ln(A) - ln(P)) / n(ln(1 + r/n))

Formulas where n = 1

(compounded once per period or unit t)

Calculation

Formula

Calculate accrued amount

Principal + Interest

A = P(1 + r)^{t}

Calculate principal amount

Solve for P in terms of A

P = A / (1 + r)^{t}

Calculate principal amount

Solve for P in terms of I

P = I / ((1 + r)^{t} - 1)

Calculate rate of interest

As a decimal

r = (A/P)^{1/t} - 1

Calculate rate of interest

As a percent

R = r * 100

Calculate time

Solve for t

ln is the natural logarithm

t = ln(A/P) / ln(1 + r), then also

t = (ln(A) - ln(P)) / ln(1 + r)

Continuous Compounding Formulas

(n → ∞)

Calculation

Formula

Calculate accrued amount

Principal + Interest

A = Pe^{rt}

Calculate principal amount

Solve for P in terms of A

P = A / e^{rt}

Calculate principal amount

Solve for P in terms of I

P = I / (e^{rt} - 1)

Calculate rate of interest

As a decimal

ln is the natural logarithm

r = ln(A/P) / t

Calculate rate of interest

As a percent

R = r * 100

Calculate time

Solve for t

ln is the natural logarithm

t = ln(A/P) / r

### How to Use the Compound Interest Calculator: Example

Say you have an investment account that increased from $30,000 to $33,000 over 30 months. If your local bank offers a savings account with daily compounding (365 times per year), what annual interest rate do you need to get to match the rate of return in your investment account?

In the calculator above select "Calculate Rate (R)". The calculator will use the equations: r = n((A/P)^{1/nt} - 1) and R = r*100.

Enter:

- Total P+I (A): $33,000
- Principal (P): $30,000
- Compound (n): Daily (365)
- Time (t in years): 2.5 years (30 months equals 2.5 years)

Showing the work with the formula r = n((A/P)^{1/nt} - 1):

\[ r = 365 \left(\left(\frac{33,000}{30,000}\right)^\frac{1}{365\times 2.5} - 1 \right) \] \[ r = 365 (1.1^\frac{1}{912.5} - 1) \] \[ r = 365 (1.1^{0.00109589} - 1) \] \[ r = 365 (1.00010445 - 1) \] \[ r = 365 (0.00010445) \] \[ r = 0.03812605 \] \[ R = r \times 100 = 0.03812605 \times 100 = 3.813\% \]

Your Answer: R = 3.813% per year

So you'd need to put $30,000 into a savings account that pays a **rate of 3.813% per year** and compounds interest daily in order to get the same return as the investment account.

## How to Derive A = Pe^{rt} the Continuous Compound Interest Formula

A common definition of the constant *e* is that:

\[ e = \lim_{m \to \infty} \left(1 + \frac{1}{m}\right)^m \]

With continuous compounding, the number of times compounding occurs per period approaches infinity or n → ∞. Then using our original equation to solve for A as n → ∞ we want to solve:

\[ A = P{(1+\frac{r}{n})}^{nt} \] \[ A = P \left( \lim_{n\rightarrow\infty} \left(1 + \frac{r}{n}\right)^{nt} \right) \]

This equation looks a little like the equation for *e*. To make it look more similar so we can do a substitution we introduce a variable m such that m = n/r then we also have n = mr. Note that as n approaches infinity so does m.

Replacing n in our equation with mr and cancelling r in the numerator of r/n we get:

\[ A = P \left( \lim_{m\rightarrow\infty} \left(1 + \frac{1}{m}\right)^{mrt} \right) \]

Rearranging the exponents we can write:

\[ A = P \left( \lim_{m\rightarrow\infty} \left(1 + \frac{1}{m}\right)^{m} \right)^{rt} \]

Substituting in *e* from our definition above:

\[ A = P(e)^{rt} \]

And finally you have your continuous compounding formula.

\[ A = Pe^{rt} \]

## Excel: Calculate Compound Interest in Spreadsheets

Use the tables below to copy and paste compound interest formulas you need to make these calculations in a spreadsheet such as Microsoft Excel, Google Sheets and Apple Numbers.

To copy correctly, start your mouse outside the table upper left corner. Drag your mouse to the outside of the lower right corner. Be sure all text inside the table is selected. **Using Control + C and Control + V**; Paste the copied information into cell **A1** of your spreadsheet. Formulas will only work starting in A1. You can modify the formulas and formatting as you wish.

### Calculate Accrued Amount (Future Value FV) using A = P(1 + r/n)^nt

In this example we start with a principal investment of 10,000 at a rate of 3% compounded quarterly (4 times a year) for 5 years. If you paste this correctly you should see the answer Accrued Amount (FV) = 11,611.84 in cell B1. Change the values in B2, B3, B4 and B5 to your specific problem.

Copy and paste this table into spreadsheets as explained in the above section.

Accrued Amount (FV) $ | = ROUND(B3 * POWER(( 1 + ((B2/100)/B4)),(B4*B5)),2) |

Rate % | 3 |

Principal $ | 10000 |

Compounding per year | 4 |

Years | 5 |

### Calculate Rate using Rate Percent = n[ ( (A/P)^(1/nt) ) - 1] * 100

In this example we start with a principal of 10,000 with interest of 500 giving us an accrued amount of 10,500 over 2 years compounded monthly (12 times per year). If you paste this correctly you should see the answer for Rate % = 2.44 in cell B1. Change the values in B2, B3, B4 and B5 to your specific problem.

Copy and paste this table into spreadsheets as explained in the above section.

Rate % | = ROUND(B4*((POWER((B2/B3),(1/(B4*B5))))-1)*100,2) |

Accrued Amount $ | 10500 |

Principal $ | 10000 |

Compounding per year | 12 |

Years | 2 |

### Further Reading

Tree of Math: Continuous Compounding

^{1}Excel^{®} is a registered trademark of Microsoft Corporation

## FAQs

### How much will $1000 saved at 5% interest for 5 years grow to? ›

In 5 years, you'll have **$11,000**.

**How much will $10,000 be worth in 20 years? ›**

With that, you could expect your $10,000 investment to grow to $34,000 in 20 years.

**How long will it take $10000 to double if it is invested at 6% interest compounded continuously? ›**

This means that the investment will take about **12 years** to double with a 6% fixed annual interest rate.

**How much is 1000 worth at the end of 2 years if the interest rate of 6% is compounded daily? ›**

Hence, if a two-year savings account containing $1,000 pays a 6% interest rate compounded daily, it will grow to **$1,127.49** at the end of two years.

**Is it possible to save $100,000 in 5 years? ›**

**If you can afford to put away $1,400 per month, you could potentially save your first $100k in just 5 years**. If that's too much, aim for even half that (or whatever you can). Thanks to compound interest, just $700 per month could become $100k in 9 years.

**Is it possible to save 1 million dollars in 5 years? ›**

The number might seem impossible, but **you can accomplish it**. To save $1 million in five years, you will have to calculate how much you will need to save and which investments can help you reach that goal. Use the tips below to start your journey toward $1 million.

**How long to save $1 million in 10 years? ›**

In order to hit your goal of $1 million in 10 years, SmartAsset's savings calculator estimates that you would need to save around **$7,900 per month**. This is if you're just putting your money into a high-yield savings account with an average annual percentage yield (APY) of 1.10%.

**How much is $100 at 10% interest at the end of each year forever worth today? ›**

Present value of perpetuity:

So, a $100 at the end of each year forever is worth **$1,000** in today's terms.

**How much will $1 million dollars grow in 10 years? ›**

Bank Savings Accounts

As noted above, the average rate on savings accounts as of February 3^{rd} 2021, is 0.05% APY. A million-dollar deposit with that APY would generate **$500 of interest after one year** ($1,000,000 X 0.0005 = $500). If left to compound monthly for 10 years, it would generate $5,011.27.

**How long will it take to double $100 dollars invested with a 7% interest rate using the Rule of 72? ›**

It will take a bit over 10 years to double your money at 7% APR. So 72 / 7 = **10.29 years** to double the investment.

### How long will it take $4000 to double itself if it is invested at 8% simple interest? ›

time=**12.** **5years**.

**How much would $200 invested at 6 interest compounded annually be worth after 6 years? ›**

Hence, it is worth **$283.70**, when $200 is invested at 6% interest compounded annually, after 6 years.

**What is the future value of $100 invested at 10% simple interest for 2 years? ›**

Answer: If the Interest Rate is 10 Percent, then the Future Value in Two Years of $100 Today is **$120**.

**How much interest does $100000 earn in a year? ›**

How much interest can $100,000 earn in a year? If you put $100,000 in CDs, high-yield savings or a money market account for a year, you could earn anywhere from **$3,000 to $5,000** based on current interest rates.

**How much interest will $200 000 earn in a year? ›**

Below is how much interest you could earn on $200,000 on an annual basis, from **1% all the way up to a 10% interest rate**: $200,000 x 0.01= $2,000. $200,000 x 0.02= $4,000. $200,000 x 0.03= $6,000.

**How to invest $100 000 to make $1 million? ›**

**Invest $400 per month for 20 years**

If you're earning a 10% average annual return and investing $400 per month, you'd be able to go from $100,000 to $1 million in savings in just over 20 years. Again, if your actual average returns are higher or lower than 10% per year, that will affect your timeline.

**How much do I need to save to be a millionaire in 5 years? ›**

Account balance | Cumulative amount invested | |
---|---|---|

After two years | $354,549 | $315,660 |

After three years | $553,370 | $473,490 |

After four years | $768,096 | $631,320 |

After five years | $1,000,000 | $789,150 |

**Is having 100K by 30 good? ›**

That's pretty good, considering that **by age 30, you should aim to have the equivalent of your annual salary saved**. The median earnings for Americans between 25 and 34 years old is $40,352, meaning the 16 percent with $100,000 in savings are well ahead of schedule. How much should you have stashed away at other ages?

**Can I retire on $2 million at 65? ›**

**Yes, for some people, $2 million should be more than enough to retire**. For others, $2 million may not even scratch the surface. The answer depends on your personal situation and there are lot of challenges you'll face. As of 2023, it seems the number of obstacles to a successful retirement continues to grow.

**How many Americans have $5 million in savings? ›**

How many $4 or $5 millionaires are there in the US? Somewhere around 4,473,836 households have $4 million or more in wealth, while **around 3,592,054** have at least $5 million. Respectively, that is 3.48% and 2.79% of all households in America.

### At what age can you retire with $1 million dollars? ›

$1 million doesn't go nearly as far in retirement as it once did. In fact, a recent survey found that investors believe they'll need at least $3 million to retire comfortably. But retiring with $1 million is still possible, even **as early as age 55**, if you're smart about it.

**Will $10 million dollars last a lifetime? ›**

Simply put, **most people should have no problem retiring at 30 with $10 million**. If you invest your money and earn a modest return, $10 million should be enough to retire and never have to work again. Of course, that doesn't mean that running out of money would be impossible.

**How many people have $3,000,000 in savings? ›**

**1,821,745 Households** in the United States Have Investment Portfolios Worth $3,000,000 or More.

**Can 2 million dollars last a lifetime? ›**

A retirement account with $2 million should be enough to make most people comfortable. With an average income, you can expect it to last **35 years or more**.

**What is 6% interest on $10000 for 5 years? ›**

An investment of $10000 today invested at 6% for five years at simple interest will be **$13,000**.

**What is the future value of $100 invested at 10 simple interest for 1 year? ›**

How much will there be in one year? The answer is $110 (FV). This $110 is equal to the original principal of $100 plus $10 in interest. **$110** is the future value of $100 invested for one year at 10%, meaning that $100 today is worth $110 in one year, given that the interest rate is 10%.

**How long in years will it take $50000 placed in a savings account at 10% interest to grow into $75000? ›**

Hence, the time will be **4.25 years**.

**Am I rich if I have $10 million dollars? ›**

**You might need $5 million to $10 million to qualify as having a very high net worth** while it may take $30 million or more to be considered ultra-high net worth. That's how financial advisors typically view wealth.

**Where do millionaires keep their money? ›**

Millionaires have many different investment philosophies. These can include investing in **real estate, stock, commodities and hedge funds**, among other types of financial investments. Generally, many seek to mitigate risk and therefore prefer diversified investment portfolios.

**How many people have $1000000 in savings? ›**

In fact, statistically, **around 10%** of retirees have $1 million or more in savings.

### What is the rule of 69? ›

The Rule of 69 is **used to estimate the amount of time it will take for an investment to double, assuming continuously compounded interest**. The calculation is to divide 69 by the rate of return for an investment and then add 0.35 to the result.

**What is the rule of 42 in investing? ›**

The so-called Rule of 42 is one example of a philosophy that **focuses on a large distribution of holdings, calling for a portfolio to include at least 42 choices while owning only a small amount of most of those choices**.

**What is Rule 72 in finance? ›**

Do you know the Rule of 72? It's **an easy way to calculate just how long it's going to take for your money to double**. Just take the number 72 and divide it by the interest rate you hope to earn. That number gives you the approximate number of years it will take for your investment to double.

**How much would $150 invested at 8 after 17 years? ›**

A sum of money (i.e. Principal) is $\$ 150$ which is invested at compounded interest (which means we have to use the above formula) at $8\% $ per annum for 17 years. Hence, if $\$ 150$ is invested at $8\% $ interest compounded continuously then its worth after 17 years will be **$ \$ 555 $**.

**How long will it take 1000 dollars to double if it is invested at 6% interest compounded semi annually? ›**

The answer is: **12 years**.

**What ROI would I need if I need to double my money in 8 years? ›**

For example, with a **9%** rate of return, the simple calculation returns a time to double of eight years.

**How much is $1000 worth at the end of 2 years if the interest rate of 6% is compounded daily? ›**

Hence, if a two-year savings account containing $1,000 pays a 6% interest rate compounded daily, it will grow to **$1,127.49** at the end of two years.

**How much would $120 invested at 6 after 21 years? ›**

Binayaka C. Investment of $120.00 will yield **$421.72** after 21 years.

**What would the future value of $100 be after 5 years at 10% compound interest? ›**

Answer and Explanation: The $100 investment becomes **$161.05** after 5 years at 10% compound interest.

**Can I live off interest on a million dollars? ›**

**Once you have $1 million in assets, you can look seriously at living entirely off the returns of a portfolio**. After all, the S&P 500 alone averages 10% returns per year. Setting aside taxes and down-year investment portfolio management, a $1 million index fund could provide $100,000 annually.

### How much will you have in 10 years if you invest $10000 today at 10% interest? ›

If you invest $10,000 today at 10% interest, how much will you have in 10 years? Summary: The future value of the investment of $10000 after 10 years at 10% will be **$ 25940**.

**How much interest will 1 million dollars earn? ›**

Bank Savings Accounts

As noted above, the average rate on savings accounts as of February 3^{rd} 2021, is 0.05% APY. A million-dollar deposit with that APY would generate **$500 of interest after one year** ($1,000,000 X 0.0005 = $500). If left to compound monthly for 10 years, it would generate $5,011.27.

**How to save $1 million dollars in 5 years? ›**

**Tips for Saving $1 Million in 5 Years**

- Capitalize on Compound Interest. ...
- Leverage Your Job. ...
- Establish Daily, Weekly and Monthly Savings Goals. ...
- Identify Ways to Increase Your Income. ...
- Find Simple Investments to Grow Your Money. ...
- Cut Expenses.

**Can you live off interest of 2 million dollars? ›**

At $200,000 per year in average returns, this is more than enough for all but the highest spenders to live comfortably. **You can collect your returns, pay your capital gains taxes and have plenty left over for a comfortable lifestyle**. The bad news about an index fund is the variability.

**Can you live off 10 million dollars interest? ›**

**It's entirely possible to live off the interest earned by a $10 million portfolio**, depending on how much you need and what your investment choices are. You'll want to make sure that your lifestyle goals are in line with the income produced if you're going to make it through retirement without running out of funds.

**How much interest does $3 million dollars earn per year? ›**

A typical stock dividend portfolio will earn between 2% and 5% in dividends each year. Additionally, the portfolio may grow over time to provide higher dividends and capital gains in the future. On a $3 million portfolio, you can expect to receive **$60,000 to $150,000 per year**. Real estate investment trust (REIT).

**How much interest will I earn with 10 million dollars? ›**

On average, dividend stock investors earn between 2% to 5% in dividends each year. So, with a $10 million portfolio, you would earn between $200,000 to $500,000 per year.

**How long will it take $1000 to double at 5% interest? ›**

Answer and Explanation: The answer is: **12 years**.

**What is the future value of $1000 after 5 years at 8 per year? ›**

An investment of $1,000 made today will be worth **$1,480.24** in five years at interest rate of 8% compounded semi-annually.

**What would $10,000 become in 5 years at 6 interest? ›**

An investment of $10000 today invested at 6% for five years at simple interest will be **$13,000**.

### What's the future value of $1000 invested at 10% for five years? ›

Using the above example, the same $1,000 invested for five years in a savings account with a 10% compounding interest rate would have an FV of $1,000 × [(1 + 0.10)^{5}], or **$1,610.51**.