Hello, I have raised this question on Google due to a dispute with my
math teacher about annuities. The questions and my calculations are as
follow:

Question 1
As retirement approaches, Rob wants to buy an annuity consisting of 10
annual payments of $8,000, the first payment to be 4 years from today.
How much will the annuity cost today if interest is 7%?

Programmed Solution 

a)   	[END]
	P/Y=1
	C/Y=1
	I/Y=7%
	N=10
	PMT= - 8000
	FV=0

PV= - 56.188.65

b)	[END]
	P/Y=1
	C/Y=1
	I/Y=7%
	N=4
	PMT= 0
	FV= 56.188.65

Answer: PV= - 42.866.05
	
Question 2
As retirement approaches, Thomas wants to buy an annuity consisting of
15 annual payments of $1,000, the first payment to be 4 years from
today. How much will the annuity cost today if interest is 8%?

Programmed Solution 

a)   	[END]
	P/Y=1
	C/Y=1
	I/Y=8%
	N=15
	PMT= - 1000
	FV=0

PV= - 8.559.48

b)	[END]
	P/Y=1
	C/Y=1
	I/Y=8%
	N=4
	PMT= 0
	FV= 8.559.48

Answer: PV= - 6.291.48


Please tell me if my calculations are wrong and why. Thank you.

For question 1:
PV=FV/((1+r)^t)

so, take the sume of this for years 4 through 13.
i.e.  PV = (8000/1.07^4)  +  (8000/1.07^5)  + (8000/1.07^6) ...

The answer one gets is $45,866.68

Questions 2 requires the same approach as question 1.

so, take the sume of this for years 4 through 18.
i.e.  PV = (1000/1.08^4)  +  (1000/1.08^5)  + (1000/1.08^6) ...

=6794.79

Ubiquity is correct on both counts.

Thank you both.
ubiquity, which button should I hit to pay for the answer?

dude, i am not an official google answerer (thats why is appears as a
comment).  Just some dude bored at work.  Keep ur money.