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hello sir, i am having some issues regarding 2 questions in this chapter on the practice questions here.
1) what is the present value of $2000 per annum, receivable for a total of 8 years with the first receipt being in 3 years time, with interest rate at 5% per annum?
i would have normally estimated that the first issue is in the 3rd year and last in 8th year. so to calculate the PV i would subtract the 8th year annuity with the 2nd year and multiply the difference with 2000.
But the available solution says that the last issue is in 10 years.
Can you please explain me what to do? take last issue to be 8 or 10? and if it is 10 then why is it so?
2) what is the present value of $6000 per annum, first receivable immediately, and thereafter in perpetuity, with interest rate at 9.5% per annum?
Solution available: $6000*1/0.095
= 63158 + 6000
= $69158Why has 6000 been added? the formula says P = A/R
1. The first receipt is indeed in 3 years time. The second receipt is in 4 years time, the third is in 5 years time, and so on. Since there are 8 receipts in total, the last receipt is in 10 years time.
2. Multiplying by 1/r gives the PV assuming that the first receipt is in 1 years time.
Here, there is also a receipt of 6,000 immediately, and the PV of 6,000 received immediately is 6,000.I don’t think you have watched the free lectures (because both of these are explained in the lectures) and I do suggest that you do watch them.
sir. concerning the queation above… that formulae is new to me of 6000*1/0.095. i do not understand how 95/100= 0.095 and not 0.95..
and can you kindly fill in the figures of the above question in the formulae i understand best of 1-(1+r)^-n/r so i can get the final answer of 69158.If the formula is new to you then you cannot possibly have watched my lectures, and you cannot expect me to type them all out here.
1/r is the formula for a perpetuity. 9.5% = 9.5/100 = 0.95
6000 + 6000*1/0.095 = 69158
The formula you quote is that for an annuity which is of no relevance to a perpetuity (and is rarely needed in the exam anyway because you are given tables).
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