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Hi Sir. I asked this question yesterday however I cannot add further comment anymore from the previous thread.
What is the amount to be invested today to receive $2,000 per annum for 9 years starting with the first receipt beginning in 4 years’ time. The interest is assumed to be 5% per annum.
A. $10,600
B. $11,200
C. $11,700
D. $12,200Your answer was as follows:
The first receipt is in 4 years time. There are 9 receipts in total, so the last receipt is in 12 years time.
Therefore we need the total factor for years 4 to 12. We get this by taking the total factor for 1 to 12 (the 12 year annuity) and subtracting the total for 1 to 3 (the three year annuity).
So: (8.863 – 2.723) x 2000 = 12,280
Which i agree.Sir, however, i wonder, do we still need to present value the $12,280 to time 0?
So, will it be $12,280 x 0.864 = $10,607? Thus the the answer being A $10,600Thank you sir
The 12,280 is already the PV at time 0, because the flows have all been discounted using the annuity factors.
The alternative was of getting the same answer is to multiply by the 9 year annuity factor and then multiply by the 3 year present value factor, because the annuity starts three years later (time 4 instead of time 1).
So 2,000 x 7.108 x 0.864 = 12,283. (The tiny difference is simply due to rounding – the tables are rounded to 3 decimal places)
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