Deposits of $7 for 45 years...

[Of course]

Deposits of $7 are made at the end of each year for 45 years at interest i. At the end of the 45 years, the value in the account is worth X. She uses that amount to buy a perpetuity that will give her $75.60 each year, using i. Find X.

Got $1200

[Wannabe Actuary]

With rounding that's what I get now...pretty sure that's what I got then as well. I remember doing this problem with high confidence.

[Wannabe Actuary]

doing this way in the middle I get (1 + i)^45 = 9.8, but I KNOW I had it equal to 10 on the exam, and that gives me 1199.xx

With the 9.8 I get something a little but lower, but still close enough that one would say 1200.

Is it possible one of the numbers you're posting here is slightly off?

But I do agree 1200 was what I put on the exam

[appleapple]

I don't remember the exact numbers in the problem, but I remember my answer was 1200.

[Of course]

Originally Posted by Wannabe Actuary

Is it possible one of the numbers you're posting here is slightly off?

No I think these were the numbers.

Thats how I did it:
N =45
PV=0
PMT=7
FV=1200 (I tried them all)
CPT I/Y -> 5.25%

5.25*1.2=6.3%

75.6/0.063 = 1200!

the other answers did not match so $1200 it is.

[Wannabe Actuary]

Here's how to set up the problem:

7 (s angle 45)at i = 75.60/i

we all know (s angle 45) = [(1 + i)^45 - 1]/i

i's in the denominator cancel, it's algebra at that point to solve for i.

Take that i and plug that back into your calculator, 7 as payment, 45 as n, computer future value.....

I got 1199-----------1200 as my answer

[vihav]

i thought the perpetuity was valued with an interest of 2i...

[Wannabe Actuary]

Nope, interest rate i....the first post here describes the problem well.

[Exam Punk]

Originally Posted by vihav

i thought the perpetuity was valued with an interest of 2i...

I remember some problem had interest rate of 2i but I can't remember which one. If it was not this one it was one very similar to this.

[Wannabe Actuary]

Originally Posted by Exam Punk

I remember some problem had interest rate of 2i but I can't remember which one. If it was not this one it was one very similar to this.

I remember that one too, it was a different one.