Calculator Soup^{®}

Current Calculation:

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

- 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)]

- 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)

- 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

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): 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" From *http://www.CalculatorSoup.com* - Online Calculator Resource.