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Hi professor
First of wish to thank you for the great lectures you are offering to us students, they are really of great help to us.
Was going through some MCQs and got stuck on the below:
Peter plans to buy a holiday villa in five years time for cash.He estimates the cost will be 1.5m. He plans to set aside the same amount of funds each year for 5 years starting immediately earning a rate of 10%interest per annum compound.
To the nearest 100, how much does he need to set aside each year.
Can you please explain the logic on how to work the above, as cannot understand answer provided on text book.
Thanks in advance
Johann
The present value of the 1.5M in 5 years has to be the same as the PV of the total amount set aside.
To get the PV of the 1.5M you simply multiply by the normal 5 year discount factor at 10%.
For the amount set aside each year, suppose it is X per year.
They set aside X immediately, so the present value of this is X.
They set aside X a year for another 4 years, and so the PV of this is X time the 4 year annuity discount factor at 10%.
You then add the two together to get the total PV, make it equal to the PV of the 1.5M, and then you can calculate X 🙂
(Questions like this are very rare in Paper F9 – it is more of a Paper F2 question)
Thanks professor now it is much clearer 🙂
You are welcome 🙂