C2: Nov 2001 #27

[Sam (Retired)]

A man turns 40 today and wishes to provide supplemental retirement income of 3000 at
the beginning of each month starting on his 65 th birthday. Starting today, he makes
monthly contributions of X to a fund for 25 years. The fund earns a nominal rate of 8%
compounded monthly.
Each 1000 will provide for 9.65 of income at the beginning of each month starting on his
65 th birthday until the end of his life.
Calculate X.
(A) 324.73
(B) 326.89
(C) 328.12
(D) 355.45
(E) 450.65

The answer is A

I use BA-35 calculator to do this question, but I cannot get the answer, can anyone help?

Thank

[shluffer]

The trick to this one is to determine the value of the fund that supplies his benefit of 3000. You have to realize that

Each 1000 will provide for 9.65 of income at the beginning of each month starting on his
65 th birthday until the end of his life.

tells us that 3000/9.65 *1000 is the amount needed in the acount to pay out the future benefit. so you just set it up in your calculator:

n = 25*12
i = 8/12
fv = -3000/9.65*1000
2nd bgn
cpt pmt

and you get A.

[Gandalf]

You need 3000 * 1000 / 9.65 at age 65 = 310880.80

The accumulated value of 1 per year, paid monthly starting at time 0, at 65 is 79.78055

The annual contribution, payable monthly is 310880.80 / 79.78055 = 3896.70.

Divide by 12 to get 324.73 per month.

[retaker]

..once again, the question could have been written a little clearer, but.....
..(Let me put on my actuarial PC hat) ...... it's no big deal. (actually, in this case it isn't that big of a deal)

"Each 1000 will provide for 9.65 of income at the beginning of each month starting on his.."

Each 1000, as of when? Each 1000 of premium paid during the first 25 years?

This wording might help one solve it faster, but I'm not saying they should have used this wording.


A man turns 40 today and wishes to provide supplemental retirement income of 3000 at the beginning of each month starting on his 65 th birthday. Starting today, he makes monthly contributions of X to a fund for 25 years. The fund earns a nominal rate of 8%
compounded monthly. At the end of the 25 years, each 1000 of the accumulated value of his fund will provide for 9.65 of income at the beginning of each month starting on his 65 th birthday until the end of his life. Calculate X.
(A) 324.73
(B) 326.89
(C) 328.12
(D) 355.45
(E) 450.65