Terms

Loan Amortization

Future value of periodic payments

1. Payment due at end of periods
   $\mathrm{F}\mathrm{V}=\mathrm{P}\mathrm{V}{(1+\frac{r}{k})}^{nk}+\mathrm{P}\mathrm{M}\mathrm{T}{\displaystyle \frac{(1+r\text{∕}k{)}^{nk}-1}{r\text{∕}k}}$

2. Payment due at beginning of period
   $\mathrm{F}\mathrm{V}=\mathrm{P}\mathrm{V}{(1+\frac{r}{k})}^{nk}+\mathrm{P}\mathrm{M}\mathrm{T}{\displaystyle \frac{(1+r\text{∕}k{)}^{nk}}{r\text{∕}k}}(1+{\displaystyle \frac{r}{k}})$

3. if $r=0$
   $\mathrm{F}\mathrm{V}=\mathrm{P}\mathrm{V}+\mathrm{P}\mathrm{M}\mathrm{T}\times nk$

$\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{d}$

1. $\mathrm{F}\mathrm{V}=\mathrm{P}\mathrm{V}\times {(1+\frac{r}{k})}^{nk}$, where $r$ is the nominal rate

2. $\mathrm{F}\mathrm{V}=\mathrm{P}\mathrm{V}\times (1+R{)}^n$, where $R$ is the effective rate

Equal repayment of principal

1. $\mathrm{P}\mathrm{M}\mathrm{T}{}_{\text{j}}=P\times {\displaystyle \frac{1+(nk-j+1)r}{nk}}$

2. $\mathrm{F}\mathrm{V}{}_{\text{j}}=P\times (1-{\displaystyle \frac{j}{nk}})$, where $j$ is the number of periods