Question on ASM Manual Pg.98 Q.13

[amark82]

Mary deposits 1000 into a fund at the beginning of each year for 10 years. At the end of 15 years, she makes an additional deposit of X.

At the end of 20 years, Mary uses the accumulated balance in the fund to buy a perpetuity-immediate with annual payments of 2000 per year for 10 years, and 1000 per year thereafter.

Interest is credited at an annual effective rate of 5%

Calculate X

I'm setting up my equation like this:

1000(double dot s angle 10) *1.05^10 + X*1.05^5 = 2000(a angle 10) + 1000/.05 where i =.05

My answer is X = 10,915.33

But the solution in my manual says the answer is this:

1000(double dot s angle 10) *1.05^10 + X*1.05^5 = 1000(a angle 10) + 1000/.05 where i =.05

where X = 4865.13

Why is it 1000(a angle 10) rather than 2000(a angle 10)?

Thanks.

[bmathew22]

I definitely can understand your confusion, but look at it this way. What you have written says that Mary will be getting 3000 per year for the first ten years, and then 1000 per year thereafter. The problem tells you that Mary receives 2000 for the first ten years and then 1000 thereafter which agrees with the solution. The way you set it up would be fine if you wanted to defer the perpetuity part by ten years, i.e. multiply it by v^10.

1000(double dot s angle 10) *1.05^10 + X*1.05^5 = 2000(a angle 10) + (V^10)*1000/.05 where i =.05

[amark82]

Thanks. After I saw your explanation, I realized I forgot to discount the perpetuity back to time zero. So,

1000(double dot s angle 10) *1.05^10 + X*1.05^5 = 2000(a angle 10) + 1000/.05 * v^10 where i =.05

which gives me X = 4,865.13

Two different ways to solve the same problem......gotta love it.

[amark82]

Opps. I didn't read your post in its entirety.