diff --git a/Grade 10/Math/MCR3U7/Unit 2: Sequences, Series, and Financial Applications.md b/Grade 10/Math/MCR3U7/Unit 2: Sequences, Series, and Financial Applications.md index 7936cdb..fa13ddb 100644 --- a/Grade 10/Math/MCR3U7/Unit 2: Sequences, Series, and Financial Applications.md +++ b/Grade 10/Math/MCR3U7/Unit 2: Sequences, Series, and Financial Applications.md @@ -16,7 +16,7 @@ **infinite series**: infinite series have **infinite** number of terms. - eg. $`1 + 2 + 3 + \cdots`$ -Terms in a sequence are numbered with subscripts: $~t_1, t_2, t_3, \cdots t_n`$ where $`t_n`$is the general or $`n^{th}`$ term. +Terms in a sequence are numbered with subscripts: $`t_1, t_2, t_3, \cdots t_n`$ where $`t_n`$is the general or $`n^{th}`$ term. **Series**: A series is the sum of the terms of a sequence. @@ -129,7 +129,7 @@ $`\large I = Prt`$ - $`r`$ is the annual interest rate expressed as a decimal (the percent is $`1 - r`$) - $`t`$ is the time in years. -- This interest is calculated from the original amount each time. (eg. if you had $$`100`$, and your interest is $`1\%`$, your interest will be a constant $$`1`$ each time.) +- This interest is calculated from the original amount each time. (eg. if you had $100, and your interest is 1\%, your interest will be a constant $1 each time.) The total amount would be $`P + I`$. @@ -167,4 +167,12 @@ Since it is basically the summation of a geometric sequence, we can apply the ge ```math \large FV = \frac{R[(1+\frac{r}{n})^n - 1]}{\frac{r}{n}} +``` + +## Present Value Annuities +The **Present Value** of an annuity is today's value of having equally spaced payments or withdrawals of money sometime in the future. + +```math +\large +PV = \frac{R[1 -(1+\frac{r}{n})^{-n}]}{\frac{r}{n}} ``` \ No newline at end of file