TVM question from qbank question, receive, interest, investor, payments

kim226

Hi guys i have 2 questions from qbank based on TVM
1st Question:
An annuity will pay eight annual payments of $100, with the first payment to be received one year from now. If the interest rate is 12% per year, what is the present value of this annuity?
A) $1,229.97.
B) $556.38.
C) $496.76.

2nd Question
An investor will receive an annuity of $5,000 a year for seven years.
The first payment is to be received 5 years from today. If the annual interest rate is 11.5%, what is the present value of the annuity?
A) $13,453.
B) $15,000.
C) $23,185.

Both questions have the first payment to be received from today/now. However the answers from both questions use the different ‘n no. of years’
Ans for 1st Question :
N = 8; I/Y = 12%; PMT = $100; FV = 0; CPT → PV = $496.76.
Ans for 2nd Question:
PMT = 5,000; N = 7; I/Y = 11.5; value (at t = 4) = 23,185.175.
Therefore, PV (at t = 0),
N = 4; I/Y = 11.5%; FV = 23,185.175; CPT → PV = $15,000.68.
I’m confused as for Question 1, qns states ‘pay eight annual payments of $100, with the first payment to be received one year from now’ and n = 8
But for Question 2, qns states ‘first payment is to be received 5 years from today’ and n =4
Any easier way to understand both questions so that i can assign the values to n?
Thanks

mnieman

Because by first calculation of 2nd qst you find annuity value at the end of 4 period, not 5. So you discount using n = 4. The same is with the first questions, your first payment is at the end of 1 year, but you find value of annuity at the 0 period, or N = 0 (present value).

waldziuchna

Just to add on, i like to ask for question 2, why n is not equals to 5 but the answer uses n=4?