FDNBUSM 02 · Compound Interest and Equivalent Rates

12.6825%

EAR = (1 + .12/12)^12 − 1 = .12682503. Monthly compounding makes EAR exceed the nominal quote.

(1.12)^(1/12) − 1 ≈ 0.948879%

An effective annual rate already includes compounding; taking the twelfth root preserves the annual accumulation factor.

i = 2% per quarter; n = 12 quarters

Convert annual nominal rate by four, and multiply years by four. The units of i and n must match.

At the end of month 18

A minimum target requires the next complete credit period. Rounding to nearest month would leave the balance below target at month 17.

(1.03)^(1/3) − 1 ≈ 0.990163%

One quarter covers three months. The monthly factor cubed must equal 1.03.

j = m[(F/P)^(1/n) − 1]

The root first finds one-period effective growth; multiplying by m gives the nominal annual quote.

They earn interest for different lengths of time.

At quarter 4, the first earns four periods and the second earns two. Combining first gives the later cash flow too much interest.

It decreases.

PV = F/(1 + i)^n. A larger n enlarges the divisor when i > 0.