Assignment X2.1

It's not clear to me why the monthly compared to lump sum would have a higher effective charge % deducted over 5 years?
The initial charges on both would be the same amount, I understand that.
However when you pay monthly then the fund is smaller, so the fund growth is smaller, so smaller annual fund charges deducted compared to a lump sum. Therefore I don't get how it would be a 2.5%pa effective charge compared to 1.5%pa?

So if you pay monthly then it's £2000 invested in year 1 compared to £10,000 in the lump sum.
Initial charges ignored for now.
Growth of 5% on the £2000 makes it £2100. Fund charge of 1% = £21.
Lump sum £10,000, growth 5% makes it £10,500. Fund charge 1% = £105.

Do this over 5 years and clearly annual charges on lump sum are higher overall.

 

Hi, I'd really appreciate the thoughts of an acted tutor here. It seems obvious to me more charges would be deducted from the lump sum rather than regular premium, with all else being equal. So why does the question say higher effective charge from the regular premium?

 

Hi. OK yes I see the required calc now. However your answer falls short of the 1.55% that it states in the question? Also the lump sum effective charge is quite short of 2.5%... I can appreciate you've done it annually not monthly but still...?

I interpreted the situation in the question as saying you could replace the initial and annual charges with an effective 1.55% pa charge and get to the same place at t = 5. So you'd roll up the lump sum at a factor (1-1.55%)*1.05 each year.... in other words £10,000*[(1.05)(1-1.55%)]^5 = £11,804. This does not match the £11,856 in the question, which confused me.

It seems also only on the final roll up to t = 5 does the annual payment's charges exceed the lump sum charges. Not exactly intuitive... hang on, shouldn't cell B27 be applying the annual % charge i.e. D5 not D4? When I make that correction the lump sum deducts more charges than the annual... (907 vs 721)

 

I think the question should have said 1.45% not 1.55% then?

 

Hi, sorry but I still find the statement "the average charge is higher than that quoted for a one-off investment" really unclear as that would seem to suggest we pay higher charges on the regular premium... but we don't as just £475 gets deducted as initial charges in both cases.

Anyway due to 907 > 721 then please confirm these parts in the question are also wrong then:

• Total charges for monthly contributions totalling £10,000 over 5 years have the effect of absorbing approximately 2.5% pa over the 5 year period
• Your manager has queried why , in respect of monthly investments, the effect of charges is so significant

 

No sorry your question specifies charges absorbing 1.55% pa, then incorrectly states for monthly it absorbs 2.5%. Should have said 1.42% and 1.24% respectively. So the question is wrong.

 

I think I can agree the numbers in the question (although we're not actually asked to check them and so for the time allowed in CA3 I think you would just go with them as they look reasonable to me). They are quoting reduction in yields.
11,856/10000 is the 5 year growth. Take the 5th root (and subtract one) and you get 3.46%. 5% less this is about 1.55%. Bingo.
Similarly, if you work out the projected fund value for an investment of £2000 pa paid monthly, with initial charge of 4.75% and annual charge of 0.5%, you get £10,755. Using a 5-year monthly annuity[s5(12)], the solution to 2000[s5(12)] =10755 is about i=2.5%. ie a reduction in yield of 2.5%.
Hope this helps.

 

Anacts, yes that's the only way you can match the numbers in the question, thanks. However their sentence in the question which talks about charges absorbing % of the fund is very clumsy & misleading. You can only absorb what's there. As is the unnecessary effective charge % higher on annual premium talk, which overcomplicates the situation etc. no doubt all this & acted's solution generally would trouble the supposed manager in the actuary department , who wouldn't even get the terms premium and lump-sum.