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CH7 Q4 Perpetuities

M

Molly

Ton up Member
Hi all,

Am getting a little confused on the rules surrounding time units here.

for example in this question we are given an annuity paying £40 at the end of each month forever with i^4=10%.

my instinct was to have all units in quarters
so
payments in quarters = 4*40=160 per quarter
then can keep i^4 as is
and use
160*a^p_inf]=160/i^p=160/0.1=1600

this is wrong and the solutions convert use monthly units - i am unsure why this is? please could someone help?

Thanks
 
Molly said:
Hi all,

Am getting a little confused on the rules surrounding time units here.

for example in this question we are given an annuity paying £40 at the end of each month forever with i^4=10%.

my instinct was to have all units in quarters
so
payments in quarters = 4*40=160 per quarter
then can keep i^4 as is
and use
160*a^p_inf]=160/i^p=160/0.1=1600

this is wrong and the solutions convert use monthly units - i am unsure why this is? please could someone help?

Thanks
Click to expand...
Hi Molly, your approach doesn't work because (a) you've used the wrong number of months per quarter, and (b) you've ignored interest between the time that each payment is made and the end of the quarter.

With three months per quarter, we cannot say that 40 at the end of each month is the same as 120 at the end of each quarter. For example, this incorrectly says that 40 at months 1, 2 and 3 is the same as 120 at month 3. In reality, the 40 at months 1 and 2 would need interest applying until month 3 to get the equivalent value at that time.

I hope this helps but do let me know if not.

Thanks,
Richie
 
Richie Holway said:
Hi Molly, your approach doesn't work because (a) you've used the wrong number of months per quarter, and (b) you've ignored interest between the time that each payment is made and the end of the quarter.

With three months per quarter, we cannot say that 40 at the end of each month is the same as 120 at the end of each quarter. For example, this incorrectly says that 40 at months 1, 2 and 3 is the same as 120 at month 3. In reality, the 40 at months 1 and 2 would need interest applying until month 3 to get the equivalent value at that time.

I hope this helps but do let me know if not.

Thanks,
Richie
Click to expand...
Hi Richie, That does help, Thank you so much!! :)
 
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