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# Thread: 2005 Exam FM Sample Question 17

1. ## 2005 Exam FM Sample Question 17

To accumulate 8000 at the end of 3n years, deposits of 98 are made at the end of each of the first n years and 196 at the end of the next 2n years. The annual effective rate of interest is i. You are given (1+i)^n=2. Determine i.
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I know this question has been answered on this website before, but I'm just wondering why my answer isn't right.

Shouldn't this work...

98 S(3n,i) + (v^n) 98 S(2n,i) = 8000

Isn't this considered a deferred annuity since the person is getting the second set of payments from time 2n to 3n??
The person will receive 98 for all 3n,
Then after n years, the person will receive 98 more for the next 2n years.
No?

2. Originally Posted by jshor101
To accumulate 8000 at the end of 3n years, deposits of 98 are made at the end of each of the first n years and 196 at the end of the next 2n years. The annual effective rate of interest is i. You are given (1+i)^n=2. Determine i.
----

I know this question has been answered on this website before, but I'm just wondering why my answer isn't right.

Shouldn't this work...

98 S(3n,i) + (v^n) 98 (2n,i) = 8000

Isn't this considered a deferred annuity since the person is getting the second set of payments from time 2n to 3n??
The person will receive 98 for all 3n,
Then after n years, the person will receive 98 more for the next 2n years.
No?

8000 is accumulated amount.
So, 98 a(3n,i) + (v^n) 98 a(2n,i) = 8000 (v^3n)
OR
98 S(3n,i) + 98 S(2n,i) = 8000

3. Get rid of the red:

98 S(3n,i) + (v^n) 98 S(2n,i) = 8000

Your accumulating, so either bring all the payments back to time 0, and then to time 3n, or take everything to 3n.

4. Thanks- I think I get it...

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