Compound interest describes how quickly an investment increases in value when interest is paid, or compounded, not only on the original amount invested but also on all interest payments that have been previously made.
This concept relates to the formula (1+i) t X through the variables i , the interest rate, and t , the amount of years (time) X dollars is invested. The first year X dollars are invested the payoff is (1+i)X. If we allow this investment to 'roll-over' another year and invest (1+i)X we will have (1+i)(1+i)X = (1+i) 2 X at the end of year two. That is we earn interest on the principal and interest from the previous year. After t years we have (1+i) t X.
The present value model simply rearranges the equation above to make it easier to transform future amounts of money into present amounts of money. Instead of using the formula (1+i) t X to calculate the 'future value' of X dollars today we can write the formula as X /(1 + i ) t to calculate how much X dollars in the future is worth to us today.
For example, assume I offer you $1100 a year from now or $1000 today that you can't spend for a year (you must save the $1000). Also, assume the current interest rate iS10%. Which would you choose Your answer should be it doesn't matter which I give you. If you take the $1000 today it is worth $1100 a year from now. Thus, the offer of $1100 in the future is equivalent to $1000 (= X /(1 + i ) = $1100/1.1).
A yearly dividend of $2 on a $35 share of stock equals a 5.71% annual rate of return ($2/$35 =.0571 = 5.71%).
If stocks returning 12 percent annual rates of return became available, investors would sell shares of Rogue Designs and buy shares in companies earning thE12% return. This would cause the price of Rogue Designs stock to fall. Note that as the stock price falls, the annual percentage return from owning Rogue Designs stock will rise, assuming the $2 annual dividend continues. Eventually the rates of return of the two (or more) similar companies should equalize.
The future value ( FV ) of the investment is calculated using the formula of future value model. The formula for this is given as:
"X " is the amount of money today
" i " is the interest rate.
" t " is the duration or the number of years.
Thus, future value of the investment is $116. 985.