Identify the known values: principal (P), interest (I) or final amount (A), time (t), and compounding frequency (n)
Choose the interest type:
Simple interest
Compound interest
Simple interest formula:
I = P × r × t
r = I / (P × t)
r = (A − P) / (P × t)
Simple interest with annual rate and time in years:
Use t in years (convert from months/days as needed)
Compound interest formula:
A = P × (1 + r/n)^(n×t)
r = n × ( (A/P)^(1/(n×t)) − 1 )
Compound interest when interest is given as I:
A = P + I
Substitute A into the compound formula to solve for r
Use consistent units:
Ensure t is in years if using n as “times per year”
Convert time to years if needed
Common compounding frequency values:
n = 1 (annual)
n = 12 (monthly)
n = 4 (quarterly)
n = 365 (daily, if applicable)
If solving for r, isolate r using the appropriate formula and compute
For percentage rate:
r_percent = r × 100
For effective annual rate (if needed from a nominal rate):
Effective annual rate = (1 + r_nominal/n)^n − 1