Deferred annuity problem

tklopfstein

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Jul 16, 2005
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Hello Anybody, please:

Myself and four study partners tried to work on this problem with no luck. I called my professor and no luck getting a hold of him

Here is the problem:

The terms of a single parent's will indicate that a child will receive an ordinary annuity of $16000.00 per year from age 18 to age 24(so the child can attend college) and that the balance of the estate goes to a niece. If the parent dies on the child's 14th birthday, how much money must be removed from the estate to purchase the annuity? ( Assume an interest rate of 6% compounded annually)

The answer in the back of the book says: $74, 993.20

We had set the problem up as so: A(n,k)= R*(1-(1+i)^-n)*(1+i)^-k/i

16000*((1-(1+.06)^(-14)))*(1+.06)^(-8)/.06

this did not come out right, we also tried 6 and 14 and 18 and 6 and 13 and 6 and various other combinations and just could not get it come out right. Please help.
We have a test tomorrow.

Tammy Klopfstein
 
Hello. The answer can be worked out as follows.

This PVIFA table gives the present value factor at birthday 17 of 7 annual payments from birthday 18 to birthday 24 as 5.5823. Multiply by 16,000 to get PV = 89,316.80 at age 17. To buy this annuity 3 years earlier at age 14 when the parent dies, the cost is PV/(1.06^3) = PV/1.191016 = 89,316.80/1.191016 = 74,992.08.

Using your formula for A(n,k), here n = 7 and k = 3.
 
Hello Jake,

Thank you for your response. I just wonder how come it doesn't work out to be the answer in the back of the book?

Tammy
 
Jake, my bad, you were totally right I worked it out on my calculator. thank you so much!

Tammy
 
I find these a bit easier going backwards.

What is PV of 7 annual payments of 16000 at rate of 6%?
Answer: 16000(1 - 1/1.06^7) / .06 = 89318.10

What is PV of 89318.10 due in 3 years at rate of 6%?
Answer: 89318.10 / 1.06^3 = 74993.20
 
I wonder if you are taking 18 the year it begins - 14 the year the parent dies and adding 3 for the price to buy it to equal 7????
 
tklopfstein said:
I understand how you got 3 for k but I don't understand how you got 7 for n.
7 annual payments from 18 to 24. I counted them on my fingers (really) because the calculation 7 = 24 - 18 + 1 has never been automatic with me. :)
 
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