For in GOD we live, and move, and have our being.

- Acts 17:28

The Joy of a Teacher is the Success of his Students.

- Samuel Chukwuemeka

### Symbols and Meanings

- You can verify all answers with the Mathematics of Finance Calculator
- To solve for a specified variable for each formula, please review Solved Examples - Literal Equations
- $A$ = amount or future value (in dollars, naira, any currency)
- $P$ = principal or present value (in dollars, naira, any currency)
- $r$ = annual interest rate (in percent)
- $m$ = number of compounding periods per year
- $t$ = time (in years)
- $i$ = annual interest rate per period
- $n$ = total number of compounding periods

If Compounded: | $m$ = |
---|---|

Annually | $1$ ($1$ time per year) |

Semiannually | $2$ ($2$ times per year) |

Quarterly | $4$ ($4$ times per year) |

Monthly | $12$ ($12$ times per year) |

Weekly | $52$ ($52$ times per year) |

Daily (Ordinary) | $360$ ($360$ times per year) |

Daily (Exact) | $365$ ($365$ times per year) |

(1.) $ A = P\left(1 + \dfrac{r}{m}\right)^{mt} $

(2.) $ P = \dfrac{A}{\left(1 + \dfrac{r}{m}\right)^{mt}} $

(3.) $ r = m\left[\left(\dfrac{A}{P}\right)^{\dfrac{1}{mt}} - 1 \right] $

(4.) $ r = m\left[10^{\dfrac{\log \left(\dfrac{A}{P}\right)}{mt}} - 1 \right] $

(5.) $ t = \dfrac{\log \left(\dfrac{A}{P}\right)}{m\log \left(1 + \dfrac{r}{m}\right)} $

(6.) $ A = P(1 + i)^n $

(7.) $ i = \dfrac{r}{m} $

(8.) $ n = mt $

(9.) $ A = Pe^{rt} $

(10.) $ P = \dfrac{A}{{e^{rt}}} $

(11.) $ t = \dfrac{\ln \left({\dfrac{A}{P}}\right)}{r} $

(12.) $ r = \dfrac{\ln \left({\dfrac{A}{P}}\right)}{t} $

(13.) $ APY = \left(1 + \dfrac{r}{m}\right)^{m} - 1 $

(14.) $ r = m\left[(APY + 1)^{\dfrac{1}{m}} - 1\right] $

(15.) $ APY = e^r - 1 $

(16.) $ r = \ln[APY + 1] $

For ACT Students

The ACT is a timed exam...$60$ questions for $60$ minutes

This implies that you have to solve each question in one minute.

Some questions will typically take less than a minute a solve.

Some questions will typically take more than a minute to solve.

The goal is to maximize your time. You use the time saved on those questions you
solved in less than a minute, to solve the questions that will take more than a minute.

So, you should try to solve each question __correctly__ and __timely__.

So, it is not just solving a question correctly, but solving it __correctly on time__.

Please ensure you attempt __all ACT questions__.

There is no "negative" penalty for any wrong answer.

**
Solve all the word problems.
Use at least two methods as applicable.
Check your solutions as applicable.
Show all Work.
Round all answers to two decimal places.
**