At time 0, George pays 1000 for a perpetuity-immediate which makes annual payments. The first payment is for X, the second payment is for 2% greater than the first, the third payment is for 3% less than the second, the fourth payment is 2% greater than the third, the fifth payment is 3% less than the fourth, the sixth payment is 2% greater than the fifth, and so on. Alternating between a 2% greater and 3% less on the previous payment. Assuming an annual effective interest rate of 8%, find X. (a) 81.58 (b) 84.29 (c) 93.67 (e) 109.14 Note: I found it easier to view the payments as two streams...payments made in even years (i.e. 2, 4, 6, 8, and so on) and payments made in odd years (i.e. 1, 3, 5, 7, and so on). Notice, if you break-up the payments this way, then the present value of each stream becomes geometric. (d) 105.45
At time 0, George pays 1000 for a perpetuity-immediate which makes annual payments. The first payment is for X, the second payment is for 2% greater than the first, the third payment is for 3% less than the second, the fourth payment is 2% greater than the third, the fifth payment is 3% less than the fourth, the sixth payment is 2% greater than the fifth, and so on. Alternating between a 2% greater and 3% less on the previous payment. Assuming an annual effective interest rate of 8%, find X. (a) 81.58 (b) 84.29 (c) 93.67 (e) 109.14 Note: I found it easier to view the payments as two streams...payments made in even years (i.e. 2, 4, 6, 8, and so on) and payments made in odd years (i.e. 1, 3, 5, 7, and so on). Notice, if you break-up the payments this way, then the present value of each stream becomes geometric. (d) 105.45
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:At time 0, George pays 1000 for a perpetuity-immediate which makes annual payments. The first
payment is for X, the second payment is for 2% greater than the first, the third payment is for 3%
less than the second, the fourth payment is 2% greater than the third, the fifth payment is 3% less
than the fourth, the sixth payment is 2% greater than the fifth, and so on. Alternating between a
2% greater and 3% less on the previous payment.
Assuming an annual effective interest rate of 8%, find X.
(a) 81.58
(b) 84.29
(c) 93.67
(e) 109.14
Note: I found it easier to view the payments as two streams...payments made in even years (i.e. 2, 4,
6, 8, and so on) and payments made in odd years (i.e. 1, 3, 5, 7, and so on). Notice, if you break-up
the payments this way, then the present value of each stream becomes geometric.
(d) 105.45
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