Stuck-up with this question

[jeetenge]

Hi everyone,

I am stuck-up with this question on Page 175 Question No 6.9 in the Course Material.

It says that it is an 1000 is invested in an fixed interest security s.t we will recieve 40 at the end of each half year and money back on redemtion in 12 years. We deposit all of the proceeds in bank account at i = 8% pa.

To calculate the money in the bank account after 10 years, I first found out the money received from the fixed interest security at the end of 12 years.

i.e. C = 80 *12 + 1000 then found out the money in the bank account as

C*(1+i)^10*8%

The Solution given in the book is

80(s10(2))*8%

Not able to get the logic of the solution

 

[Phil]

Hi jeetenge

Here is where you are going wrong:

To calculate the money in the bank account after 10 years, I first found out the money received from the fixed interest security at the end of 12 years.

Have you misunderstood the question?
It is NOT asking what will be in the bank account 10 years after redemption of the fixed interest security.
It is asking what will be in the bank account 10 years from now/Date 0

Another point - when a question says you intend to do something with the proceeds of a security....it usually means as soon as each cashflow is realised.....it usually doesn't mean you'll wait until the final cashflow before taking the action. But pay close attention to the question to be sure.


Step 1: Identify what cashflows are going into/out of the account in question, in the period in question
Answer: We're interested in the first 10 years of the bank account
During those 10 years, £40 has been pumped into it half yearly
So you could scribble out the 1st sentence of this question and the bit about your money back on redemption in 12 years.

Step 2: Think of the annuity notation that corresponds to this
Answer:

80(s10(2))*8%

-------------------

And even if the question was asking "what will be in the bank account 10 years after redemption of the fixed interest security?" Your method would have been wrong because

C = 80*12 + 1000

is what everything would have accumulated to at the end of 12 years if there was NO interest. Whilst there is interest *8%

If you calculated C * 8% and then did your

C*(1+i)^10*8%

bit that would be the correct answer to this question you were thinking of


Hope this helps