Chapter 4

4.2 Payment less frequent than interest period.

One payment period $r$ = Several interest periods $k$.

• total times $n$, $n=rk$.
• Calculate $I=(1+i)^k-1$,interest rate per payment period. Since there is k times interest periods in $1$ payment period.
  

Annuity Immediate:

1. Present Value is $a$ _{${\overline{r|}}I$} = a_{${\overline{n|}}i$} / $S$_{${\overline{k|}}i$}
   

2. Feture Value is $S$ _{${\overline{r|}}I$} = S_{${\overline{n|}}i$} / $S$_{${\overline{k|}}i$}
   

3. $(1+I)^r=(1+i)^n$

Annuity Due:

1. ${\ddot {a}}$ _{${\overline{r|}}I$} = $a$ _{${\overline{n|}}i$} / $a$ _{${\overline{k|}}i$}
   

2. ${\ddot {S}}$ _{${\overline{r|}}I$} = $S$ _{${\overline{n|}}i$} / $a$ _{${\overline{k|}}i$}
   

3. ${\ddot {a}}$ _{${\overline{r|}}I$} = $(1+I)a$ _{${\overline{r|}}I$}
   

Perpetuity:

$a$ _{${\overline{∞|}}I$} = 1/ a_{${\overline{k|}}i$}

4.3 Annuity with payments More frequent than each interest period:

One interest periods = Multiple payment periods.

1. determine payment period rate, $J=(1+i)^{\frac{1}{m}}-1=\frac{i^{(m)}}{m}$

chapter 5, Loan Repayment

5.2 Amortized loans and Amortization Schedule 分期付款:

N number of years m number os compound payment per year. principal payment = payment amount - interest;

• Amortization schedule shows the time and amount of each payment, devision of the payment into interest and principal, and the OLB after each payment.
  loan, -PV, FV = 0

Amortization schedule R<Q