I am having a lot of trouble with annuities so far. I cannot seem to determine whether to use annuity due or annuity immediate if it's not stated in the question directly.
Here is a question I am trying to answer.
"Chuck needs to purchase an item in 10 years. The item costs 200 today, but its price inflates at 4% per year.
To finance the purchase, Chuck deposits 20 into an account at the beginning of each year for 6 years. He deposits an additional X at the beginning of years 4,5 and 6 to meet his goal.
The annul effective interest rate is 10%.
Calculate X."
Here was my approach using the block payment shortcut (s_n denotes s angle at n, annuities immediate):
200(1.04)^10 = 20s_10 + Xs_7 - (20+X)s_5.
Solving for x in this case does not yield the correct answer. Where am I going wrong when I try to apply the block payment shortcut?
I also tried it using another method. Simply using my comparison time at t=5 and accumulating the AV of 5 to 10.
So at t=0,1,2 a payment of 20 was made and at t=3,4,5 a payment of 20 + X was made. Using the block method again, I want to accumulate these payments to t=5 and then accumulate it to 10 by multiplying it by (1.1)^5:
(20s_5 + Xs_2) 1.1^5 = 200(1.04)^10
Which again, does not yield the correct answer. The solution used the AV of an annuities due instead, but what's the difference if I do it this way? Where am I going wrong?
Here is a question I am trying to answer.
"Chuck needs to purchase an item in 10 years. The item costs 200 today, but its price inflates at 4% per year.
To finance the purchase, Chuck deposits 20 into an account at the beginning of each year for 6 years. He deposits an additional X at the beginning of years 4,5 and 6 to meet his goal.
The annul effective interest rate is 10%.
Calculate X."
Here was my approach using the block payment shortcut (s_n denotes s angle at n, annuities immediate):
200(1.04)^10 = 20s_10 + Xs_7 - (20+X)s_5.
Solving for x in this case does not yield the correct answer. Where am I going wrong when I try to apply the block payment shortcut?
I also tried it using another method. Simply using my comparison time at t=5 and accumulating the AV of 5 to 10.
So at t=0,1,2 a payment of 20 was made and at t=3,4,5 a payment of 20 + X was made. Using the block method again, I want to accumulate these payments to t=5 and then accumulate it to 10 by multiplying it by (1.1)^5:
(20s_5 + Xs_2) 1.1^5 = 200(1.04)^10
Which again, does not yield the correct answer. The solution used the AV of an annuities due instead, but what's the difference if I do it this way? Where am I going wrong?
ASM FM 11th ed.: Solving using block payments shortcut
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