What is the compound interest of 30000?

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

Table of Contents Show

The Compound Interest Formula
Compound Interest Formulas Used in This Calculator
How to Use the Compound Interest Calculator: Example
How to Derive A = Pert the Continuous Compound Interest Formula
Excel: Calculate Compound Interest in Spreadsheets
Calculate Accrued Amount (Future Value FV) using A = P(1 + r/n)^nt
Calculate Rate using Rate Percent = n[ ( (A/P)^(1/nt) ) - 1] * 100
Further Reading
Using this compound interest calculator
What is compound interest?
Compounding investment returns
More NerdWallet calculators
Compounding with additional contributions

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

Calculate accrued amount
Principal + Interest

Calculate principal amount
Solve for P in terms of A

Calculate principal amount
Solve for P in terms of I

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

Calculate rate of interest
As a decimal

Calculate rate of interest
As a percent

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)

Calculate accrued amount
Principal + Interest

Calculate principal amount
Solve for P in terms of A

Calculate principal amount
Solve for P in terms of I

Calculate rate of interest
As a decimal

Calculate rate of interest
As a percent

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 → ∞)

Calculate accrued amount
Principal + Interest

Calculate principal amount
Solve for P in terms of A

Calculate principal amount
Solve for P in terms of I

Calculate rate of interest As a decimal

ln is the natural logarithm

Calculate rate of interest
As a percent

Calculate time Solve for t

ln is the natural logarithm

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 = Pert 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. 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/(B4B5))))-1)*100,2)
Accrued Amount $	10500
Principal $	10000
Compounding per year	12
Years	2

Using this compound interest calculator

Try your calculations both with and without a monthly contribution — say, $50 to $200, depending on what you can afford.
This savings calculator includes a sample rate of return. To see the interest you can expect, compare rates on NerdWallet.

SoFi Checking and Savings

APY

2.50%SoFi members with direct deposit can earn up to 2.50% annual percentage yield (APY) interest on all account balances in their Checking and Savings accounts (including Vaults). Members without direct deposit will earn 1.20% APY on all account balances in Checking and Savings (including Vaults). Interest rates are variable and subject to change at any time. Rates of 2.50% APY (with direct deposit) and 1.20% APY (without direct deposit) are current as of 09/30/2022. Additional information can be found at http://www.sofi.com/legal/banking-rate-sheet

LendingClub High-Yield Savings

Citizens Online Savings Account

Min. balance for APY

$5,000

CIT Bank Savings Connect

These cash accounts combine services and features similar to checking, savings and/or investment accounts in one product. Cash management accounts are typically offered by non-bank financial institutions.

Learn More

on Wealthfront's website

Wealthfront Cash Account

Read review

Aspiration Spend & Save Account - Aspiration Plus

APY

5.00%The Aspiration Save Account’s up to 5.00% Annual Percentage Yield (“APY”) with up to 71x the national interest rate is variable, subject to change, and only available to customers enrolled in Aspiration Plus after conditions are met. Customers not enrolled in Aspiration Plus receive 3.00% APY after conditions are met.

Learn More

on Betterment's website

Betterment Cash Reserve

APY

2.75%Annual percentage yield (variable) is as of 10/19/2022.

CDs (certificates of deposit) are a type of savings account with a fixed rate and term, and usually have higher interest rates than regular savings accounts.

LendingClub CD

Checking accounts are used for day-to-day cash deposits and withdrawals.

SoFi Checking and Savings

APY

Learn More

Deposits are FDIC Insured

Upgrade - Rewards Checking

Learn More

Deposits are FDIC Insured

Current Account

Learn More

Deposits are FDIC Insured

Chime Checking Account

Learn More

on Citibank, N.A.'s website

Citi Priority Account

Money market accounts pay rates similar to savings accounts and have some checking features.

UFB Elite Money Market

Here’s a deeper look at how compounding works:

What is compound interest?

For savers, the definition of compound interest is basic: It’s the interest you earn on both your original money and on the interest you keep accumulating. Compound interest allows your savings to grow faster over time.

In an account that pays compound interest, such as a standard savings account, the return gets added to the original principal at the end of every compounding period, typically daily or monthly. Each time interest is calculated and added to the account, the larger balance earns more interest, resulting in higher yields.

For example, if you put $10,000 into a savings account with a 2% annual yield, compounded daily, you’d earn $203 in interest the first year, another $206 the second year and so on. After 10 years of compounding, you would have earned a total of $2,214 in interest.

But remember, that’s just an example. For longer-term savings, there are better places than savings accounts to store your money, including Roth or traditional IRAs and CDs.

Compounding investment returns

When you invest in the stock market, you don’t earn a set interest rate but rather a return based on the change in the value of your investment. When the value of your investment goes up, you earn a return.

If you leave your money and the returns you earn invested in the market, those returns are compounded over time in the same way that interest is compounded.

If you invested $10,000 in a mutual fund and the fund earned a 7% return for the year, you’d gain about $700, and your investment would be worth $10,700. If you got an average 7% return the following year, your investment would then be worth about $11,500.

Over the years, your investment can really grow: If you kept that money in a retirement account over 30 years and earned that average 7% return, for example, your $10,000 would grow to more than $76,000.

In reality, investment returns will vary year to year and even day to day. In the short term, riskier investments such as stocks or stock mutual funds may actually lose value. But over a long time horizon, history shows that a diversified growth portfolio can return an average of 6% to 7% annually. Investment returns are typically shown at an annual rate of return.

The average stock market return is historically 10% annually, though that rate is reduced by inflation. Investors can currently expect inflation to reduce purchasing power by 2% to 3% a year.

Compounding can help fulfill your long-term savings and investment goals, especially if you have time to let it work its magic over years or decades. You can earn far more than what you started with.

More NerdWallet calculators

Compounding with additional contributions

As impressive as compound interest might be, progress on savings goals also depends on making steady contributions.

Let’s go back to the savings account example above. We started with $10,000 and ended up with about $2,214 in interest after 10 years in an account with a 2% annual yield. But by depositing an additional $100 each month into your savings account, you’d end up with about $25,509 after 10 years, when compounded daily. The interest would be about $3,509 on total deposits of $22,000.