How to use Excel's PV function when payments are made quarterly but rate is compounded semi-annually?

0

Note: This is not a plead to help with my homework

Here's the question in a book, which I'm trying to solve using Excel's PV function:

A £100 bond has one year to maturity. The bond pays 6% per year with coupon payments made quarterly. The interest rate is 5.8% per year with interest compounded semi-annually. Calculate the value of the bond.

╔═══╦══════╦═════╦══════════╦═══════════════════════╗
║   ║  A   ║  B  ║    C     ║           D           ║
╠═══╬══════╬═════╬══════════╬═══════════════════════╣
║ 1 ║Period║ Amt ║    PV    ║       Formula         ║
║ 2 ║ 0.25 ║ 1.5 ║   1.4787 ║ =B2/(1+5.8%/2)^(A2*2) ║
║ 3 ║  0.5 ║ 1.5 ║   1.4577 ║ =B3/(1+5.8%/2)^(A3*2) ║
║ 4 ║ 0.75 ║ 1.5 ║   1.4370 ║ =B4/(1+5.8%/2)^(A4*2) ║
║ 5 ║    1 ║ 1.5 ║   1.4166 ║ =B5/(1+5.8%/2)^(A5*2) ║
║ 6 ║    1 ║ 100 ║  94.4429 ║ =B6/(1+5.8%/2)^(A6*2) ║
║ 7 ║      ║     ║          ║                       ║
║ 8 ║      ║ Val ║ 100.2330 ║ =SUM(C2:C6)           ║
╚═══╩══════╩═════╩══════════╩═══════════════════════╝

I understand the formula, but I'm not able to use the PV function to get the result. Here's what I tried:

=PV(5.8%/2,4,1.5,100)
# Result: 94.78

As I understand,

  • the first argument should be the rate (divided by the number of compoundings in a year)
  • the second should be the number of periods (which in this case is 4 - 4 quarterly payments in a year)
  • the annuity payment made during each period
  • the future value paid / received after the payment of last annuity

I think the discrepancy has to do with the fact that the payments are made quarterly and the discount rate is compounded semi-annually; I don't understand it, though.

Popeye_The_Sailorman

Posted 2018-07-24T08:34:06.837

Reputation: 11

Do you have to use the PV function or be open to something else? – Mark Fitzgerald – 2018-07-24T09:24:24.587

@MarkFitzgerald, I'm not doing this to accomplish some temporary task. I wanted to learn working with Excel's financial functions. So, I want to use PV. However, if you have any other method, please feel free to add it as an answer; it might give me more clarity. – Popeye_The_Sailorman – 2018-07-24T09:28:37.897

Why don't you try this one, =PV(5.8%/2,12/3,100) where 5.8%/2 is semiannual rate, 4 is 4 payments in year (quarterly) & 100 is PMT, it returns 372.60 – Rajesh S – 2018-07-24T12:57:47.687

No answers