RatedrillCompound interest
Compound interest is interest earned on both the principal and the interest already added: A = P x (1 + r/n)^(n x t), where n is the number of compounding periods per year. The interest earned is A minus P. More frequent compounding at the same nominal rate gives a slightly larger result.
Syntax
A = P x (1 + r/n)^(n x t) (interest = A - P)| Part | What it is |
|---|---|
P | Starting principal |
r | Nominal annual rate as a decimal |
n | Compounding periods per year (1 yearly, 4 quarterly, 12 monthly, 365 daily) |
t | Number of years |
Examples
P = 1,000, r = 5%, yearly, 3 years
A = 1,000 x 1.05^3Result: A = 1,157.63; interest = 157.63
Excel: =FV(5%, 3, 0, -1000)
P = 1,000, r = 6%, monthly, 2 years
A = 1,000 x (1 + 0.06/12)^24Result: A = 1,127.16
Excel: =FV(6%/12, 24, 0, -1000)
P = 2,000, r = 8%, yearly, 10 years
A = 2,000 x 1.08^10Result: A = 4,317.85
Common mistakes
- Forgetting to divide the rate by n when compounding monthly (using 6% per month instead of 0.5%) produces an absurdly large answer.
- Dividing the rate by 12 but leaving t in years (exponent 2 instead of 24) understates growth; the exponent must be the total number of periods.
- Reporting A as the interest: the interest earned is A minus the principal.
Practice Compound interest
These drills check your answer on live data, free, no account needed.
- Future value of a lump sumYou deposit $1,500 in an account that earns 3.25% per year, compounded annually. You make no other deposits or withdrawals. How much is in the account after 30 years?
- Monthly compoundingYou put $1,000 into a certificate of deposit that pays 2.25% APR, compounded monthly. What is it worth after 20 years?
- Simple vs compound interestTwo accounts each start with $2,000 and earn 3.25% per year for 20 years. Account A pays simple interest. Account B compounds annually. How much more does Account B hold at the end?
Questions
What is the compound interest formula for monthly compounding?
A = P x (1 + r/12)^(12 x t). For 1,000 at 6% for 2 years: 1,000 x 1.005^24 = 1,127.16.
How do I calculate compound interest in Excel?
Use =FV(rate per period, number of periods, 0, -principal). For yearly compounding at 5% for 3 years on 1,000: =FV(5%, 3, 0, -1000) returns 1,157.63.
Related
- Simple interestSimple interest is principal times rate times time (I = P x r x t). Worked examples for years, months and days, the Excel formula and the mistakes to avoid.
- Future valueHow to calculate the future value of a lump sum with FV = PV x (1 + r)^n, step-by-step examples, the Excel FV function with its sign convention, and errors.
- Effective annual rateThe effective annual rate turns a nominal rate with monthly, quarterly or daily compounding into the true yearly rate: (1 + i/m)^m - 1. Examples and Excel.
- Rule of 72The rule of 72 estimates doubling time as 72 divided by the rate. Examples at 6%, 9% and 18%, how accurate it is, the exact ln(2) formula and Excel NPER.