View Full Version : Annuity Homework Problem

12-07-2010, 09:53 PM
Sunrise Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research, Jill Moran. Ms. Moran will retire at the end of exactly 15 years. Upon retirement, she is entitled to receive an annual end-of-year payment of $40,000 for exactly 20 years. If she dies prior to the end if the 20-year period, the annual payments will pass to her heirs. During the 15 year "Accumulation period" Sunrise wishes to fund the annuity by making equal annual end-of-year deposits into an account earning 10% interest. Once the 20-year "distribution period" begins, Sunrise plans to move the accumulated monies into an account earning a guaranteed 7% per year. At the end of the distribution period, the account balance will equal 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 16.


A. Draw a time line depicting all of the cash flows associated with Sunrise's view of the retirement annuity.

B. How large a sum must Sunrise accumulate by the end of year 15 to provide the 20-year, $40,000 annuity?

C.How large must Sunrise's equal annual end-of-year deposits into the account be over the 15-
year accumulation period to fund fully Ms Moran's retirement annuity?

D.How much would Sunrise have to deposit annually during the accumulation period if it could
earn 12% rather than 10% during the accumulation period?

E.How much would Sunrise have to deposit annually during the accumulation period if Ms.
Moran's retirement annuity was a perpetuity and all other terms were the same as initially

I know this can't be that hard but i'm having trouble starting it. Can someone just help me start it please?


12-07-2010, 11:57 PM
What formulas are you using?
Do you know what the "present value of an annuity" means?

40000(1 - 1/1.07^20) / .07 will give you the amount required at end of 15 years;
do you follow that?

12-10-2010, 01:40 AM
yes i do follow that. so you doing present value? It kind sound like a Future value problem.

12-10-2010, 09:29 AM
OK; 40000(1 - 1/1.07^20) / .07 = 423,760.57;
that's the amount that will permit 20 payments of $40,000.

So you need to calculate the annual deposit (over 15 years, at 10%)
that will accumulate to $423,760.57; that's where FV comes in;
A = Annual deposit, F = 423760.57 :
A = F(.10) / (1.10^15 - 1)

Notice that the "trick" is to work this in reverse:
1: F = what is needed in 15 years
2: A = annual deposit to reach F

12-10-2010, 06:25 PM
ok is this right?

C. 423760/31.772=13337.52

D. 423760/37.280=11366.95

E. 40,000/.07= 571428.5714

571428.5714/31.772= 17985.28803

12-11-2010, 01:32 AM
All correct; good job !

12-11-2010, 01:57 PM
thanks for the help!