📘 Chapter 6: Time Value of Money Part II
Quick Guide: New Variables & Rates
Chapter Add-OnsPMT (Payment): Use Excel PMT() with (rate, nper, pv, [fv], [type]).
Distinguish between Annuity (type=0) and
Annuity Due (type=1).
Ordinary Annuity (type = 0)
Blue marker jumps at the end of period t ⇒ Excel type=0.
Annuity Due (type = 1)
Pink marker jumps at the beginning of period t ⇒ Excel type=1.
APR — Annual Percentage Rate
Nominal yearly rate quoted by banks/lenders. It does not include compounding, so
typically APR ≤ EAR. Monthly rate = APR/12.
Bankers usually tell you APR; you won’t get the true annual return (EAR) from them.
Excel (convert APR → EAR): =EFFECT(nominal_rate, npery)
EAR — Effective Annual Rate
The right annual return including compounding. For APR compounded m times/year:
EAR = (1 + APR/m)^m − 1
Example: APR = 12%, monthly (m=12) →
EAR = (1 + 12%/12)^12 − 1 = 12.68%
Excel: =EFFECT(12%, 12) ⇒ 12.68%
(Reverse, if you ever need nominal from EAR:
APR = m * ((1+EAR)^(1/m) − 1). Excel: =NOMINAL(EAR, m))