QM1_Time value of Money

Effective annual rate(EAR)

For discrete compounding

• Where: m is the compounding frequency
  • r is the noinal/quoted/stated annual interest rate
  • r/m is periodic interest rate

For continuous compounding

• 时时刻刻分分秒秒在计息.
• 例: 算名义年利率是8%, 求连续计算情形下的EAR.
  • 计算器按法: 0.08 --> 2ND --> LN ==>结果: 1.083287

Conversion of PV/FV

Present Value (PV)

• The value of an initial investment.

Future Value (FV)

• The value of an initial investment would be worth n period from today.

Conversion of PV/FV:

• compounding:
  • 
• continuous compounding:
  • 
• 站在今天去推测未来会价值几何: PV --> FV : 复利
• 站在未来推测今天需要存入多少: FV --> PV :折现

Annuity

Ordinary annuity

• all constant cash flows occuring at the end of each period(END), 后付年金

Annuity due

• all constant cash flows occuring at the beginning of each period(BEG), 先付年金
• 

Prepetuity

• a set of constant never-ending sequential cash flows occuring at the end of each period, 永续年金
  • PV = A/R
    • where A: the periodic payment
    • r: the periodic return