Retirement annuity

hinanifaf · 02-11-2010, 03:08 PM

Good morning
Mr T retires end of exactly 12yrs,and he is entitled to receive an annual end of year payment of 42000 for exactly 20yrs.During the 12yr accumulation period, he wishes to fund the annuity by making equal annual end-of-year deposits into an account earning 10% interest.Once the 20yrs distribution period begins,he is planning to move the accumulated monies into an account earning a guaranteed 15% per year.At the end of the distribution period,the account balance will equal to zero.Note that the first deposit will be made at the end of year 1 and the first distribution payment will be received at the end of year 13.

> What is the sum that he must accumulate by the end of year 12 to provide the 20year, 42000 annuity?
> What will be the annual end-of-year deposits that must be made into the account over the 12yr accumulation period to fund fully his retirement annuity?
> What will be his annual deposit during the accumulation period if it could earn 12% rather than 10% during the accumulation period?
> What will be the annual deposit if it was a perpetuity and all other terms wer the same as initially described?
Anyone who can assist me in this as all this sounds the same to me.
Thanks

hinanifaf · 02-24-2010, 12:19 AM

<blockquote id="quote">quote<hr height="1" noshade id="quote">Originally posted by hinanifaf
 Good morning
Mr T retires end of exactly 12yrs,and he is entitled to receive an annual end of year payment of 42000 for exactly 20yrs.During the 12yr accumulation period, he wishes to fund the annuity by making equal annual end-of-year deposits into an account earning 10% interest.Once the 20yrs distribution period begins,he is planning to move the accumulated monies into an account earning a guaranteed 15% per year.At the end of the distribution period,the account balance will equal to zero.Note that the first deposit will be made at the end of year 1 and the first distribution payment will be received at the end of year 13.
> What is the sum that he must accumulate by the end of year 12 to provide the 20year, 42000 annuity?FVA = PMT X FVIFA
> What will be the annual end-of-year deposits that must be made into the account over the 12yr accumulation period to fund fully his retirement annuity?FVA = PMT X FVIFA PMT = FVA/FVIFA
> What will be his annual deposit during the accumulation period if it could earn 12% rather than 10% during the accumulation period? PVA = PMT X PVIFA
> What will be the annual deposit if it was a perpetuity and all other terms wer the same as initially described?PVIFA=1/IX42000
Anyone who can assist me in this - PLEASE comment on the formula next to the question.
Many Thanks
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june23am · 02-26-2010, 10:50 PM

assalamualikum, i think you hav't got the case properly, if a person is to entitle for annual payments for 20 years after retirement than i m very much sure that business from where mr t is to retire of, will invest or accumulate profit to make year end payments of 42000 12 years from now till 20 years which makes it a complete priod of 32 year from today 12+20. this is what i have realized form the questions you have posted under the detail.
for first 12 year company is to accumulate profit to have sufficient fund from which starting period or payment will be financed. it is that first company will invest some amount today for 12 years, as per the question 12 end of year payments will be made by business to accumulate profit at 10%...and than after 12 years total accumulated amount will be invested to provide 42000 anually to mr T at 15%. now thing is first we have to calculate what accumulated profit we need after 12 years from now to get 42000 in return, for this first to calculate total amount to accumulate by end of year 12..at 15% interest, which is PVn= PMT*(PVIFAi%,20) so PV20= 42000*6.2593 = 262892....so for your first question answer is 262892 is the sum must accumulate by end of year 12
question 2 > What will be the annual end-of-year deposits that must be made into the account over the 12yr accumulation period to fund fully his retirement annuity?
for this annual end of year payment will be calculated as PMT= 262892/(FVIFi%,12years)...so 262892/21.3842 = 12293.75 almost...

> What will be his annual deposit during the accumulation period if it could earn 12% rather than 10% during the accumulation period?
answer is. same as above 262892/FVIFi%, 12years) but this time instead of 10% rate of interest (i%) will be used 12%..

> What will be the annual deposit if it was a perpetuity and all other terms wer the same as initially described?

initial depsoit if annuity is perpetuity and initial deposit earns 10% PVperp =PMT 8 (1/i) so = 420008(1/.15)=280000

and end of year deposit
PMT = FVAn / (FVIFAi%, 12years) so 280000 /21.3842 = 13093.78 are end of year deposits for 12 years..hope you understand it now jazakALLAH

<blockquote id="quote">quote<hr height="1" noshade id="quote">Originally posted by hinanifaf
 Good morning
Mr T retires end of exactly 12yrs,and he is entitled to receive an annual end of year payment of 42000 for exactly 20yrs.During the 12yr accumulation period, he wishes to fund the annuity by making equal annual end-of-year deposits into an account earning 10% interest.Once the 20yrs distribution period begins,he is planning to move the accumulated monies into an account earning a guaranteed 15% per year.At the end of the distribution period,the account balance will equal to zero.Note that the first deposit will be made at the end of year 1 and the first distribution payment will be received at the end of year 13.

> What is the sum that he must accumulate by the end of year 12 to provide the 20year, 42000 annuity?
> What will be the annual end-of-year deposits that must be made into the account over the 12yr accumulation period to fund fully his retirement annuity?
> What will be his annual deposit during the accumulation period if it could earn 12% rather than 10% during the accumulation period?
> What will be the annual deposit if it was a perpetuity and all other terms wer the same as initially described?
Anyone who can assist me in this as all this sounds the same to me.
Thanks
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hinanifaf · 03-02-2010, 04:53 PM

thank you so much,i just didn't add the years thats were my figures went wrong, the rest is okay.