Effective Rate of Interest – The Real Cost of Borrowing

When you borrow money, the lender quotes a nominal interest rate — say, 12% per annum. But if interest is compounded more than once a year (monthly, quarterly, half-yearly), the actual interest you pay over one year ends up being more than 12%. That actual, real rate is the Effective Rate of Interest.

Think of it this way: if the bank charges you interest every month, then after the first month you owe a little more, and the next month's interest is calculated on that bigger amount. So you're paying "interest on interest" even within a single year. The effective rate captures this compounding effect.

The Precise Definition

The Effective Annual Rate (EAR) — also called the Effective Rate of Interest — is the annual interest rate that would give the same final amount if compounding were done only once per year, as the nominal rate gives when compounded $m$ times per year.

Why It Matters

Suppose you invest ₹1,00,000 at a nominal rate of 12% p.a., compounded monthly.

• Nominal rate = 12% → you might think you'll earn ₹12,000 in one year.
• Actual calculation: monthly rate = $12\%/12 = 1\% = 0.01$. After 12 months:

So you actually earned ₹12,682.50 — that's an effective rate of 12.6825%.

The difference of ₹682.50 is the "interest on interest" you wouldn't get if compounding were annual.

Key Exam Points

• If compounding is annual ($m=1$), effective rate = nominal rate.
• As $m$ increases (more frequent compounding), the effective rate increases — but it approaches a limit (continuous compounding gives $e^r - 1$).
• For loans, the effective rate is always greater than or equal to the nominal rate (equal only when $m=1$). …