finance Q: funding retirement plan w/ annual EOY dep's @ 5%

[bsimmons]

Sunrise Industries wishes to accumulate a retirement fund for its vice president of research, Jill Moran. Ms. Moran, by contract, will retire at the end of exactly 12 years. Upon retirement, she is entitled to receive an annual end-of-year payment of $42,000 for as long as she lives, and to her university thereafter.

During the 12-year "accumulation period" Sunrise wishes to fund the retirement plan by making equal, annual, end-of-year deposits into an account earning 5% interest. Once "distribution period" begins, Sunrise plans to move the accumulated monies into an account earning a guaranteed 9% per year.

Note that the first deposit will be made at the end of year 1 and that the first distribution payment will be received at the end of year 13.

How large a sum must Sunrise accumulate by the end of year 12 to provide the 20-year, $42,000 retirement benefit? How large must Sunrise's equal, annual, end-of-year deposits into the account be over the 12-year accumulation period to fund fully Ms. Moran's retirement annuity?

I believe this is the equation PV=C/r-g(1-(1+g/1+r) ^N)= C/r-g(1-0)=C/r-g. I just not sure. Any help would be gladly appreciated

 

[Denis]

Re: I cant figure this one out. Finance Question.

Go in reverse:

Step#1: calculate PV of 20 annual payments of $42,000, rate 9% annual
(that'll give you the amount that must be accumulated to at end of year 12)

Step#2: calculate the necessary 12 annual deposits, rate 5%, to reach the above

You showed:
" I believe this is the equation PV=C/r-g(1-(1+g/1+r) ^N)= C/r-g(1-0)=C/r-g. "
When posting such equations, please indicate what the variables represent;
else, everyone will give up and you'll get no help; kapish?

 

[bsimmons]

Re: I cant figure this one out. Finance Question.

Thanks Denis. Looks like I was on the right track.

 

[Denis]

Re: I cant figure this one out. Finance Question.

Welcome. So you should be getting:
Step#1:
i = interest rate (.09)
d = annual deposit (42000)
n = number of years (20)
p = present value (?)
p = d(1 - k) / i where k = 1 / (1 + i)^n : that'll give you 383,398.92
Step#2:
i = interest rate (.05)
n = number of years (12)
p = calculated above
d = annual deposit (?)
d = p(i) / j where j = (1 + i)^n - 1 : that'll give you 24,087.19

In case you're interested:
you can combine the above 2 equations to get:
d = 42000(.05)(1 - k) / (.09j) : that'll give you 24,087.19