Present/Future Value

Types of interest

1. Simple interest - it is a fixed sum of money you will get based on your initial investment. eg: 4% simple interest yearly on your initial investment of $1000. How much interest is earned after 5 years?

   $$\begin{aligned} I &= 1000 \times 0.04 \times 5 = 200 \text{ dollars} \end{aligned}$$

   Formula:

   $$I = P \times r \times t$$
   1. I = Interest earned (the total amount of interest accrued)
   2. P = Principal (the initial investment amount)
   3. r = Annual interest rate (expressed as a decimal)
   4. t = Time (the number of years the amount is invested)
      

2. Compound Interest
   The formula:

   $$\begin{aligned} FV &= PV(1 + r)^t \\ \text{where:} \\ FV &= \text{future value} \\ PV &= \text{present value} \\ r &= \text{period interest rate (as decimal)} \\ t &= \text{number of periods} \end{aligned}$$
   1. Present Value is the current value - eg. your bank account current sum.
      
   2. Future Value is how much your bank account may have in the future, since bank gives you interest (though close to negligible)
      
   3. Interest rate is basically how much you would profit.
      
   4. Number of periods can be in months, years days, whatever

Couple things to note before we proceed:

We will be using Excel to solve it. If you dont have excel, please feel free to use Google Sheets. You can try using the following functions:

• RATE - Calculates the interest rate per period of an annuity
• NPER - Calculates the number of periods for an investment
• PV - Calculates the present value of an investment
• FV - Calculates the future value of an investment
  Note

  Excel sheet at end of lecture