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Compound Interest Calculator

Post on: 16 Март, 2015 No Comment

Compound Interest Equation

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

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

Calculate rate of interest in decimal, solve for r

r = n[(A/P) 1/nt — 1]

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

Calculate rate of interest in decimal, solve for r

r = (A/P) 1/t — 1

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

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.

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.