Key Terms
Perpetuity
Payments that never stop. Preferred stock: fixed-dividend stock; a common perpetuity example.
Constant perpetuity
Payment never changes. Growing perpetuity: payment increases each period by a fixed rate G.
Example
$32,000 auto loan; 6% annual; 3 years. Monthly rate = 6% / 12 = 0.5% Periods = 36 Monthly payment = $973.50
Annuity
Equal periodic payments for a fixed number of periods. Annuity due: first payment at beginning of period 1.
Ordinary annuity
First payment occurs at the END of period 1. Annuity due: first payment occurs IMMEDIATELY (beginning of period 1).
USE CASE
"How much will I have if I invest X per period for N periods?"
Lump sum offer
$787,000. Discount rate: 9%.
Loan amortization
A scheduled repayment plan that breaks each fixed payment into its interest and principal components. Each payment is th
Stated (nominal) rate
The rate advertised or printed on the contract.
Effective annual rate (EAR)
The actual rate after accounting for compounding within the year. This is the true cost of borrowing.
Stated
1.5% per month. Intuitive math: 1.5% x 12 = 18% per year.
Actual
(1.015)^12 - 1 = 0.1956 = 19.56% per year.
Annualized
7% x 52 weeks = 364% stated annual rate. Effective rate is even higher with compounding.
Annualized (no compounding)
26%. With compounding: ~29.3%.
CONSTANT PERPETUITY
PV = C / Rs GROWING PERPETUITY: PV = C / (Rs - G)