Lesson 1: Simple Interest
- Main Article: Simple Interest
Simple Interest
- where:
is the principal value/present value is the interest rate is the length of term or time in years is the simple interest
- The following formulas can be derived from the formula above:
Future Value
- where:
is the future value/maturity value is the principal value/present value is the simple interest
- The following formulas can be derived from the formula above:
in terms of , , and .
Monthly Payment
- where:
is the monthly payment is the future value/maturity value is the length of term or time in years
Lesson 2: Compound Interest
- Main Article: Compound Interest
Compounding Once a Year
- where:
is the future value/maturity value is the principal value or present value is the annual interest rate - t is the length of the term in years
- The following formulas can be derived from the formula above:
- Present Value Formula (Compound Interest)
- Time Formula (Compound Interest)
Compounding More than Once a Year
- where:
is the future value/maturity value is the principal value or present value is the annual interest rate - t is the length of the term in years
is the frequency of compounding
(how often the interest compounds)
The following formulas can be derived from the formula above:
- **Present Value Formula (Compound Interest)** $$ P = \dfrac{FV}{\left( 1 + \frac{r}{n} \right)^{nt}} $$ $$ P = FV\left( 1 + \frac{r}{n} \right)^{-nt} $$ - **Time Formula (Compound Interest)** $$ t = \frac{\log(FV) - \log(P)}{n \log\left( 1 + \frac{r}{n} \right)} $$ ### Compound Interest $$ I_{C} = FV - P $$ - where: - $I_{C}$ is the compound interest - $FV$ is the future value/maturity value - $P$ is the present value/principal value
- The following formulas can be derived from the formula above:
$$ FV = P + I _{C} $$ $$ P = FV - I_{C} $$ - $I_{C}$ in terms of $P$, $r$, $t$, and $n$. $$ I_{C} = P\left[ \left( 1 - \frac{r}{n} \right)^{nt} -1\right] $$