Finance guide

Compound Interest Examples

Q: What is a simple compound interest example?

A deposit of 1,000 USD at a fixed 6% nominal annual rate, compounded monthly for five years, becomes approximately 1,348.85 USD. Divide the annual decimal rate by twelve and count sixty monthly periods. The resulting balance includes the original deposit, so the interest portion is approximately 348.85 USD. The example excludes fees, taxes and withdrawals and keeps full precision until the reported amount is rounded.

Q: How much does depositing 200 dollars monthly for ten years produce?

With no starting balance, a 5% nominal annual rate compounded monthly and 120 end-of-month deposits of 200 USD, the modeled balance is approximately 31,056.46 USD. Deposits total 24,000 USD, and modeled interest is approximately 7,056.46 USD. These numbers assume a constant rate, every payment arriving on schedule and valuation immediately after the last payment. Changing the payment timing or using an APY as though it were a nominal rate changes the result.

Follow three checked calculations: a starting deposit, equal monthly deposits and a future payment discounted to today. Each example states the rate convention, timing and rounding before showing the result.

Published June 3, 2026. Updated October 28, 2026. Amounts use US dollars for illustration; rates are hypothetical.

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Three checked results

One-time deposit

\mathrm{FV}\approx1{,}348.85\,\mathrm{USD}

Start with $1{,}000\,\mathrm{USD}$ , use a fixed nominal annual interest rate of $6\%$ , compound monthly and leave the money for five years. There are no additional deposits or withdrawals.

See the calculation steps

End-of-month deposits

\mathrm{FV}_{\mathrm{end}}\approx31{,}056.46\,\mathrm{USD}

Start with no balance and deposit $200\,\mathrm{USD}$ at the end of every month for ten years. The nominal annual rate is fixed at $5\%$ , compounded monthly. Value the account immediately after the last deposit.

See the calculation steps

Present value

\mathrm{PV}\approx8{,}219.27\,\mathrm{USD}

Find the present value of a single $10{,}000\,\mathrm{USD}$ payment due in five years, using an annual effective discount rate of $4\%$ . There are no intermediate cash flows.

See the calculation steps

Start with matching rates and periods

Compound interest adds earned interest to the balance, allowing later interest to apply to that larger amount. The examples below hold the rate constant and assume no fees, taxes or withdrawals. They use full numerical precision internally and round reported money amounts to cents. Actual account crediting rules may produce a different statement amount.

Each symbol and the quantity it represents
Symbol	Meaning
$P$	Starting principal in the chosen currency
$r$	Nominal annual interest rate as a decimal
$m$	Compounding periods per year
$t$	Time in years
$i$	Growth rate per matching period
$N$	Number of matching growth periods
$\mathrm{PMT}$	Equal contribution each period

For a nominal annual decimal rate compounded $m$ times per year, the matching periodic rate is $i=r/m$ and the period count is $N=mt$ . Without additional cash flows, grow the principal once for every period:

\mathrm{FV}=P(1+i)^N=P\left(1+\frac{r}{m}\right)^{mt}

The monthly-deposit example has both deposits and compounding on the same monthly schedule. A different deposit schedule needs its own periodic-rate conversion or cash-flow model; do not reuse the monthly annuity formula unchanged.

Compound interest examples showing a one-time deposit, 120 end-of-month deposits and an annually discounted future payment. — Three verified time-value examples. The monthly-deposit model has no starting balance and uses 120 end-of-month payments; full accessible calculations appear below.

The formulas and results in this illustration also appear as accessible, selectable mathematics in the examples below. Open the full-size illustration.

Example 1: one deposit compounded monthly

Start with $1{,}000\,\mathrm{USD}$ , use a fixed nominal annual interest rate of $6\%$ , compound monthly and leave the money for five years. There are no additional deposits or withdrawals.

1. Convert the annual rate to a monthly decimal
The entered rate is nominal annual interest, not an already compounded annual yield. Divide its decimal form by the twelve monthly periods.
$r=0.06,\qquad i=\frac{r}{12}=0.005$
2. Count the monthly growth periods
Five full years contain sixty monthly growth periods in this simplified fixed-rate model.
$N=mt=12\times5=60$
3. Apply growth and round the final balance
Raise the monthly growth factor to the number of periods. Keep full precision inside the power and round the final currency amount to cents.
$\mathrm{FV}=1{,}000(1.005)^{60}\approx1{,}348.85\,\mathrm{USD}$
4. Separate principal from earned interest
Subtract the original deposit from the unrounded final balance, then round the interest amount for reporting.
$I=\mathrm{FV}-P\approx348.85\,\mathrm{USD}$

The balance contains $1{,}000.00\,\mathrm{USD}$ of principal and approximately $348.85\,\mathrm{USD}$ of interest. Interest is part of the final balance, so it should not be added again.

Watch the balance grow each year

These are end-of-year observations of the same monthly-compounding model. No additional principal is added. The table rounds each reported observation, while later years still use the original unrounded calculation.

End-of-year balances and cumulative interest from the initial one-thousand-dollar deposit
End of year	Balance	Cumulative interest
1	$1{,}061.68\,\mathrm{USD}$	$61.68\,\mathrm{USD}$
2	$1{,}127.16\,\mathrm{USD}$	$127.16\,\mathrm{USD}$
3	$1{,}196.68\,\mathrm{USD}$	$196.68\,\mathrm{USD}$
4	$1{,}270.49\,\mathrm{USD}$	$270.49\,\mathrm{USD}$
5	$1{,}348.85\,\mathrm{USD}$	$348.85\,\mathrm{USD}$

To reproduce this example in the calculator, choose a $1{,}000\,\mathrm{USD}$ principal, $6\%$ nominal annual interest, monthly compounding, five years and no recurring contribution.

Example 2: equal deposits at the end of each month

1. Match the deposit and compounding periods
Both events occur monthly. Use the nominal annual rate divided by twelve as the monthly decimal rate, and count one hundred twenty deposits.
$i=\frac{0.05}{12},\qquad N=12\times10=120$
2. Use the ordinary-annuity factor
End-of-period payments form an ordinary annuity. Each payment has a different number of remaining growth periods, so multiplying the total deposits by one ten-year growth factor would overstate the result.
$\mathrm{FV}_{\mathrm{end}}=\mathrm{PMT}\frac{(1+i)^N-1}{i}$
3. Substitute without rounding the monthly rate
Retain the full quotient for the monthly rate. Evaluate the power and annuity factor before rounding the final result.
$\mathrm{FV}_{\mathrm{end}}=200\frac{(1+0.05/12)^{120}-1}{0.05/12}\approx31{,}056.46\,\mathrm{USD}$
4. Report deposits and growth separately
Contributed money is not earned interest. Subtract the contributed amount from the unrounded future value before reporting the growth.
$D=120\times200=24{,}000\,\mathrm{USD},\qquad I=\mathrm{FV}_{\mathrm{end}}-D\approx7{,}056.46\,\mathrm{USD}$

The deposits total $24{,}000.00\,\mathrm{USD}$ and the modeled interest is approximately $7{,}056.46\,\mathrm{USD}$ . The final deposit earns no interest before this valuation; the first deposit earns interest for the remaining 119 months.

Beginning versus end of each month

An ordinary annuity deposits at the end of each period. An annuity due deposits at the beginning. Move the same one hundred twenty payments one month earlier and each receives one extra growth period. Use the unrounded ordinary-annuity result for the timing adjustment.

\mathrm{FV}_{\mathrm{begin}}=(1+i)\mathrm{FV}_{\mathrm{end}}\approx31{,}185.86\,\mathrm{USD}

Same monthly payments, nominal rate and valuation date with different payment timing
Payment timing	Deposits	Final balance
End of month	$24{,}000.00\,\mathrm{USD}$	$31{,}056.46\,\mathrm{USD}$
Beginning of month	$24{,}000.00\,\mathrm{USD}$	$31{,}185.86\,\mathrm{USD}$

The beginning-of-month model adds approximately $129.40\,\mathrm{USD}$ of growth without changing the contributed amount. Both balances are valued at the end of month 120. For the main end-of-month example, enter a zero starting principal, a $200\,\mathrm{USD}$ monthly contribution, $5\%$ nominal annual interest, monthly compounding, ten years and end-of-period contributions.

If a starting principal is also present, grow it for the full period and add the deposit-stream value. Adjust only the deposit term for beginning-of-period timing:

\mathrm{FV}_{\mathrm{end}}=P(1+i)^N+\mathrm{PMT}\frac{(1+i)^N-1}{i}\qquad(i\ne0)

Example 3: discount a future payment to today

Find the present value of a single $10{,}000\,\mathrm{USD}$ payment due in five years, using an annual effective discount rate of $4\%$ . There are no intermediate cash flows.

1. Identify the annual rate and horizon
The discount rate is already effective for a full year, so annual periods match the rate directly.
$i=0.04,\qquad N=5$
2. Build the five-year growth factor
Discounting reverses the growth that the same assumed rate would produce over the stated interval.
$(1+i)^N=(1.04)^5=1.2166529024$
3. Divide the future payment by the factor
Use the unrounded factor and round the present value once to cents. A different discount rate or a different payment date changes this estimate.
$\mathrm{PV}=\frac{10{,}000}{1.2166529024}\approx8{,}219.27\,\mathrm{USD}$

This is a time-value comparison under the selected discount rate. It does not establish a market price, guarantee the future payment or decide whether an investment is suitable.

Nominal annual interest is different from APY

The first example starts from a $6\%$ nominal annual rate. Because interest is compounded monthly, its effective annual yield is slightly higher. This relationship holds the nominal rate fixed while changing the compounding schedule:

\mathrm{APY}=\left(1+\frac{0.06}{12}\right)^{12}-1\approx6.1678\%

If the same nominal $6\%$ were compounded annually, the five-year balance would be approximately $1{,}338.23\,\mathrm{USD}$ instead of $1{,}348.85\,\mathrm{USD}$ . That is approximately $10.62\,\mathrm{USD}$ less. This comparison changes the effective yield; it does not hold APY constant.

When a product already quotes an effective annual decimal yield $a$ , convert it to a matching monthly rate with $i=(1+a)^{1/12}-1$ . Do not divide APY by twelve or compound it again as though it were a nominal rate. Read the APR vs APY guide for the terminology, or use the APY Calculator to compare rate conventions. A fee-inclusive lending APR is not automatically a nominal savings rate.

Check rounding and the model boundaries

The displayed money amounts are rounded to cents after the calculation. Do not truncate the monthly rate, round each growth factor or feed a rounded table balance into the next year. Those choices create a different model. Real institutions may have their own daily-accrual, crediting and rounding rules, so a statement can differ even when an educational example is internally correct.

The annuity quotient is written for $i\ne0$ . At a zero rate, add the principal and scheduled deposits directly. For a $1{,}000\,\mathrm{USD}$ starting balance and 120 payments of $200\,\mathrm{USD}$ , the zero-rate result is $25{,}000\,\mathrm{USD}$ :

\mathrm{FV}=P+N\,\mathrm{PMT}\quad(i=0),\qquad\mathrm{FV}=P\quad(N=0)

A zero period count means no scheduled contributions have occurred under this model. The worked examples use whole matching periods. Partial months, dated deposits, irregular withdrawals, changing interest rates and daily crediting need a model that states how those events are handled.

Future value is a projection under assumptions. Present value is a rate-dependent comparison, and neither result guarantees investment performance. Taxes, fees, inflation and access restrictions are excluded here. Use account disclosures to understand an actual savings product and avoid treating a fixed example rate as a promised return.

FAQ

Frequently Asked Questions

What is a simple compound interest example?

A deposit of

1{,}000\,\mathrm{USD}

at a fixed

6\%

nominal annual rate, compounded monthly for five years, becomes approximately

1{,}348.85\,\mathrm{USD}

. Divide the annual decimal rate by twelve and count sixty monthly periods. The resulting balance includes the original deposit, so the interest portion is approximately

348.85\,\mathrm{USD}

. The example excludes fees, taxes and withdrawals and keeps full precision until the reported amount is rounded.

How much does depositing 200 dollars monthly for ten years produce?

With no starting balance, a

5\%

nominal annual rate compounded monthly and 120 end-of-month deposits of

200\,\mathrm{USD}

, the modeled balance is approximately

31{,}056.46\,\mathrm{USD}

. Deposits total

24{,}000\,\mathrm{USD}

, and modeled interest is approximately

7{,}056.46\,\mathrm{USD}

. These numbers assume a constant rate, every payment arriving on schedule and valuation immediately after the last payment. Changing the payment timing or using an APY as though it were a nominal rate changes the result.

Why do beginning-of-month deposits produce a different balance?

Each beginning-of-month deposit has one more monthly growth period than the matching end-of-month deposit. Under the same positive monthly rate and the same 120 deposits, multiply the ordinary-annuity future value by

1+i

to obtain the annuity-due future value. Here the result is approximately

31{,}185.86\,\mathrm{USD}

, or

129.40\,\mathrm{USD}

more after rounding. Total contributed money stays the same; the difference comes from earlier timing, not from an extra deposit.

Can I combine a starting balance with regular deposits?

Yes. Grow the starting balance for the full interval, then add the future value of the deposit stream under its own timing convention. For matching monthly deposits and compounding, the end-of-month model adds an ordinary annuity to the initial principal term. Beginning-of-month deposits multiply only the deposit-stream term by

1+i

. The starting principal is already present at the beginning and should not receive an additional timing multiplier.

Should I divide APY by twelve to get the monthly rate?

An APY is an effective annual yield, so dividing it by twelve generally does not give the equivalent monthly growth rate. For an effective annual decimal yield

a

, the matching monthly rate is

i=(1+a)^{1/12}-1

. By contrast, the examples with monthly compounding start from a nominal annual decimal rate

r

and use

i=r/12

. A fee-inclusive lending APR is another concept and should not automatically be substituted for either savings-rate convention.

What happens when the rate or investment time is zero?

At a zero rate there is no modeled interest: the ending balance is the starting principal plus all deposits made by the valuation date. The ordinary-annuity expression contains a division by the periodic rate, so use its zero-rate case instead of substituting zero into that denominator. When the period count is zero, no scheduled monthly deposits have occurred in this model and the balance remains the starting principal.

Why can a bank statement differ from the example?

These examples hold rates constant, use matching monthly periods and round only the final reported money amount. A real account can use daily accrual, different crediting dates, dated cash flows, balance tiers, changing rates, withdrawals, fees or specified rounding rules. Compare the account disclosure and actual transaction dates before treating an illustration as a statement forecast. The examples show how the stated model works; they do not replace the product terms.

Are future value, present value and CAGR interchangeable?

They answer different questions. Future value moves a stated amount or payment stream forward under an assumed growth rate. Present value discounts future money to a stated valuation date. CAGR summarizes annualized change between positive start and end values when intermediate external cash flows are absent. None of these calculations guarantees an investment return, and a simple CAGR should not be used to attribute growth correctly when deposits or withdrawals occur during the comparison.

Related Tools

Check the examples with the matching calculator

Compound Interest Calculator

Enter principal, nominal rate, compounding and monthly contribution timing.

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Future Value Calculator

Model a current balance and scheduled contributions at a stated rate.

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Present Value Calculator

Discount a future amount under an explicit rate and time convention.

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Sources and calculation checks

The CFPB explains interest on principal and previously earned interest. Investor.gov identifies starting investment, recurring contributions, rate, time and compounding as calculator inputs. OpenStax distinguishes end-of-period annuities from annuities due. The CFPB disclosure reference explains what annual percentage yield measures. The numerical examples here were independently checked from their stated inputs.

Editorial Transparency

Who maintains this page

Ownership and review

Written and maintained by the Toolarithm editorial team. The method was last reviewed on October 28, 2026. No independent professional review is claimed.

Methodology

The editorial team checks definitions, examples, linked tools, and cited references. Dates shown here come from the page's maintained publication record.

Read the editorial methodology

Dates and sources

Published June 3, 2026. Updated October 28, 2026.

Three checked results

One-time deposit

End-of-month deposits

Present value

Start with matching rates and periods

Example 1: one deposit compounded monthly

1. Convert the annual rate to a monthly decimal

2. Count the monthly growth periods

3. Apply growth and round the final balance

4. Separate principal from earned interest

Watch the balance grow each year

Example 2: equal deposits at the end of each month

1. Match the deposit and compounding periods

2. Use the ordinary-annuity factor

3. Substitute without rounding the monthly rate

4. Report deposits and growth separately

Beginning versus end of each month

Example 3: discount a future payment to today

1. Identify the annual rate and horizon

2. Build the five-year growth factor

3. Divide the future payment by the factor

Nominal annual interest is different from APY

Check rounding and the model boundaries

Frequently Asked Questions

Related reading for the next decision

Check the examples with the matching calculator

Compound Interest Calculator

Future Value Calculator

Present Value Calculator

Sources and calculation checks

Who maintains this page

Ownership and review

Methodology

Dates and sources