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human
Why are we adding all the present values?

In the economics lecture, the instructor explained this formula

 **F = P (1+i)\^t** 

F - Future Value (return)

P - Present Value

i - interest rate

t - time period for which the money is lent

The above formula is very clear to me, it has a very straightforward meaning. 

But then he said a little transposition of the above formula makes it useful in another case:

**P = F/\[(1+i)\^t\]**

He explained, assume that a company or government promises you to have $3 per year for 5 years. At the end of 5th year it will pay you $100 (along with that $3). The discounting rate (I don't know why he didn't use the word interest rate) is 5%. So, 

&#x200B;

|Time|Final Amount F|Interest (1+i)\^t|Present Value (F/\[(1+i)\^t\]|
|:-|:-|:-|:-|
|1|$3|1.05|$2.857|
|2|$3|1.1025|$2.7210|
|3|$3|1.1576|$2.59156|
|4|$3|1.2154|$2.4683|
|5|$3, $100|1.27617|$2.3507, $78.3594|
||||Total = $91.34|

he said, the company will ask you to pay it at once those $91.34 and that is called bonds. I really didn't get what he did. Why did he add all those present values? If someone promises me to pay $100 after 5 years, and the interest rate in market is 5%, I would simply lent him, by the equation

**P = 100/\[(1.05)\^5\] = 78.3594**

Can somebody please explain what he tried to explain?
gpt
Your calculation is for a zero coupon bond - this bond pays a $3 coupon per year on top of the $100 at maturity. The difference between your figure and his figure is the value of the coupon payments.

The value of the principle is $78.35, as you calculated. The value of the coupons is $12.99 

$78.35 + $12.99 = $91.34

Essentially, the bond pays 3% interest, but market interest rate is 5%, so you’d only be willing to pay $91.34 for the bond to compensate for the low coupon. If the bond paid a $5 coupon, you’d be willing to buy it for $100.