# What is my monthly interest?

Computes the interest a savings balance earns each month and in total, at a yearly rate compounded daily, monthly, quarterly, twice a year or yearly, with an optional monthly deposit.

- Page: https://www.acalculator.org/finance/interest-calculator
- JSON spec: https://www.acalculator.org/finance/interest-calculator.json
- Version: d127aebfbde2

## Default answer

Example with the default inputs (Balance $10,000.00, Interest rate (yearly) 5%, Compounding Monthly, Added each month $0.00, Number of months 12): At 5% a year, $10,000.00 earns $41.67 of interest in the first month and $511.62 over the whole time.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| principal | Balance | The amount in the account at the start. |
| rate | Interest rate (yearly) | The nominal yearly interest rate, before compounding. |
| comp | Compounding | How many times a year interest is added to the balance: daily (365), monthly (12), quarterly (4), twice a year (2) or yearly (1). |
| deposit | Added each month | A deposit added at the end of every month. Leave it empty or 0 for none. |
| months | Number of months | How many months the balance earns interest. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| first | Interest in the first month | The starting balance × the monthly rate. |
| interest | Total interest | All the interest earned over the months. |
| average | Average interest a month | The total interest divided by the number of months. |
| last | Interest in the last month | The interest earned in the final month. |
| balance | Ending balance | The balance after the last month. |
| paidIn | Money put in | The starting balance plus every deposit. |
| monthly | Monthly rate | The rate earned each month: (1 + yearly rate ÷ m)^(m ÷ 12) − 1 for m compoundings a year. |
| apy | APY | The annual percentage yield: (1 + yearly rate ÷ m)^m − 1. |

## Method

Each month, interest = balance × ((1 + r/m)^(m/12) − 1), where r is the yearly rate and m the compoundings a year; then the deposit is added.

## Assumptions

- The rate does not change.
- Deposits are added at the end of each month.
- With daily, quarterly, twice-yearly or yearly compounding, interest builds at the equivalent monthly rate, so the balance matches P(1 + r/m)^(mt) at every compounding date.
- Tax and fees are not included.

## Worked examples

1. principal = $10,000.00, rate = 5%, comp = 12, months = 12 gives first = $41.67, interest = $511.62, balance = $10,511.62, apy = 5.11619%, last = $43.62. Source: SEC Investor.gov compound interest formula A = P(1 + r/n)^(nt) (https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator).
2. principal = $25,000.00, rate = 4%, comp = 365, months = 12 gives first = $83.47, interest = $1,020.21, apy = 4.080849%. Source: SEC Investor.gov compound interest formula with daily compounding (https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator).
3. principal = $0.00, rate = 6%, comp = 12, deposit = $100.00, months = 12 gives first = $0.00, balance = $1,233.56, interest = $33.56, paidIn = $1,200.00, average = $2.80. Source: Future value of an annuity (Microsoft Excel FV function, https://support.microsoft.com/en-us/office/fv-function-2eef9f44-a084-4c61-bdd8-4fe4bb1b71b3).
4. principal = $10,000.00, rate = 6%, comp = 1, months = 24 gives balance = $11,236.00, interest = $1,236.00. Source: SEC Investor.gov compound interest formula with yearly compounding (https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator).

## FAQ

### How do I calculate monthly interest?

With monthly compounding, divide the yearly rate by 12 and multiply by the balance. $10,000 at 5% a year earns 10,000 × 0.05 ÷ 12 = $41.67 in the first month. The next month earns a little more, because last month’s interest earns interest too: $511.62 over the first year.

### How is monthly interest worked out with daily compounding?

Interest is added every day at the yearly rate ÷ 365, so over a month the balance grows by (1 + rate ÷ 365)^(365 ÷ 12) − 1. At 4% that is 0.33387% a month: $83.47 on $25,000 in the first month.

### What is the difference between the interest rate and the APY?

The interest rate is the yearly rate before compounding. The APY (annual percentage yield) is what the balance actually grows in a year once interest earns interest: (1 + rate ÷ m)^m − 1 for m compoundings a year. 5% compounded monthly is an APY of 5.1162%. If your bank quotes an APY, use the money market or savings calculator, which take an APY.

### Why does each month earn a different amount of interest?

Because the balance grows. Each month’s interest is added to the balance, and deposits add to it too, so the next month earns interest on a larger amount. At 5% on $10,000 with no deposits, month 1 earns $41.67 and month 12 earns $43.62.

### How much interest does $100,000 earn a month?

At 5% compounded monthly, $100,000 earns $416.67 in the first month. At 4% it earns $333.33. Type your own balance and rate for your account.

### Does this work for a loan?

The first month’s interest is the same idea: a $10,000 loan at 5% a year charges about $41.67 in its first month. But loan payments lower the balance, so later months charge less. Use the amortization or loan calculator to see a loan month by month.

## Sources

- U.S. Securities and Exchange Commission, Investor.gov compound interest calculator and formula. https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator
- Consumer Financial Protection Bureau, Regulation DD (Truth in Savings), 12 CFR 1030, Appendix A: annual percentage yield. https://www.consumerfinance.gov/rules-policy/regulations/1030/a/