# Compound Interest Calculator

## Calculator Use

Calculate compound interest on an investment or savings. Using the compound interest formula, calculate principal plus interest or principal or rate or time. Includes compound interest formulas to find principal, interest rates or final investment value including continuous compounding A = Pe^rt.

## Compound Interest Equation

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

Where:

- A = Accrued Amount (principal + interest)
- P = Principal Amount
- I = Interest Amount
- R = Annual Nominal Interest Rate in percent
- r = Annual Nominal Interest Rate as a decimal
- r = R/100
- t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
- n = number of compounding periods per unit t; at the END of each period

## Compound Interest Formulas and Calculations:

- Calculate Accrued Amount (Principal + Interest)
**A = P(1 + r/n)**^{nt}

- Calculate Principal Amount, solve for P
- P = A / (1 + r/n)
^{nt}

- P = A / (1 + r/n)
- Calculate rate of interest in decimal, solve for r
- r = n[(A/P)
^{1/nt}- 1]

- r = n[(A/P)
- Calculate rate of interest in percent
- R = r * 100

- Calculate time, solve for t
- t = ln(A/P) / n[ln(1 + r/n)] = [ 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)
**A = P(1 + r)**^{t}

- Calculate Principal Amount, solve for P
- P = A / (1 + r)
^{t}

- P = A / (1 + r)
- Calculate rate of interest in decimal, solve for r
- r = (A/P)
^{1/t}- 1

- r = (A/P)
- Calculate rate of interest in percent
- R = r * 100

- Calculate time, solve for t
- t = t = ln(A/P) / ln(1 + r) = [ ln(A) - ln(P) ] / ln(1 + r)

### Continuous Compounding Formulas (n → ∞)

- Calculate Accrued Amount (Principal + Interest)
**A = Pe**^{rt}

- Calculate Principal Amount, solve for P
- P = A / e
^{rt}

- P = A / e
- Calculate rate of interest in decimal, solve for r
- r = ln(A/P) / t

- Calculate rate of interest in percent
- R = r * 100

- Calculate time, solve for t
- t = ln(A/P) / r

### Example Calculation

I have an investment account that increased from $30,000 to $33,000 over 30 months. If my local bank offers savings account with daily compounding (365), what annual interest rate do I need to get from them to match the return I got from my investment account?

In the calculator select "Calculate Rate (R)". The equation the calculator will use is: 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 (2.5 years is 30 months)

Your
Answer: R = 3.8126% per year

Interpretation: You will need to put $30,000 into a savings account that pays a rate of 3.8126% per year and compounds interest daily in order to get the same return as your investment account.

**Cite this content, page or calculator as:**

Furey, Edward "Compound Interest Calculator"; CalculatorSoup, *https://www.calculatorsoup.com* - Online Calculator