Problema Solution
The present value of 3000 per year for 8 years discounted back to the present at 9 percent
Answer provided by our tutors
The word problem statement is actually incomplete and/or in error. The phrase "present value" and "discounted back to the present" are ambiguous but we assume that there was some original value and it was discounted every year(?) at 9%. That still does not clearly make a statement about what is being solved for, so we assume that 'x' is some original value and it gets discounted by 9% every year until its value is $3,000 ... of course, '3000 per year' does not specify a value but a yearly value and so that is also ambiguous.
Let's decide that the good formula for exponential continuous discounting is:
C=e^(-rt)B
where 'C' is the current value, 'P' is the original value, 'r' is the rate and 't' is the time in years ('e' is the exponential constant)
3000 = e^(-0.09*8)B
click here to calculate the original value before any discounting
B=6163.29963
So, based on the numerous assumptions we are choosing, the undiscounted value would have approximately been 6160.