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Suppose you aim to establish a perpetuity wherein money will be withdrawn every other compounding period. For example, the investment might compound every 6 months, but funds are withdrawn once a year. (a) If R dollars are withdrawn at a rate of r%, find a formula for the present value of the perpetuity. Be sure to simplify your formula as much as possible. (b) Suppose P₁ is the present value of an annuity whose compounding term corresponds with the withdrawal term. Let P2 denote the present value of the situation described above, wherein the investment compounds twice for every withdrawal term. Which number should be larger, P₁ or P₂? Justify your response. (c) Suppose a $5000 annual scholarship is to be established. The Office of Advancement figures it can get an APR of 3% compounding semi-annually on any funds invested to support the scholarship. Determine the amount which must be invested today to support the fund.

Suppose you aim to establish a perpetuity wherein money will be withdrawn every other compounding period. For example, the investment might compound every 6 months, but funds are withdrawn once a year. (a) If R dollars are withdrawn at a rate of r%, find a formula for the present value of the perpetuity. Be sure to simplify your formula as much as possible. (b) Suppose P₁ is the present value of an annuity whose compounding term corresponds with the withdrawal term. Let P2 denote the present value of the situation described above, wherein the investment compounds twice for every withdrawal term. Which number should be larger, P₁ or P₂? Justify your response. (c) Suppose a $5000 annual scholarship is to be established. The Office of Advancement figures it can get an APR of 3% compounding semi-annually on any funds invested to support the scholarship. Determine the amount which must be invested today to support the fund.

Advanced Engineering Mathematics
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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2-57. Suppose you aim to establish a perpetuity wherein money will be withdrawn every other compounding period. For example, the investment might compound every 6 months, but funds are withdrawn once a year. (a) If R dollars are withdrawn at a rate of r%, find a formula for the present value of the perpetuity. Be sure to simplify your formula as much as possible. (b) Suppose P₁ is the present value of an annuity whose compounding term corresponds with the withdrawal term. Let P2 denote the present value of the situation described above, wherein the investment compounds twice for every withdrawal term. Which number should be larger, P₁ or P₂? Justify your response. (c) Suppose a $5000 annual scholarship is to be established. The Office of Advancement figures it can get an APR of 3% compounding semi-annually on any funds invested to support the scholarship. Determine the amount which must be invested today to support the fund.
Transcribed Image Text:2-57. Suppose you aim to establish a perpetuity wherein money will be withdrawn every other compounding period. For example, the investment might compound every 6 months, but funds are withdrawn once a year. (a) If R dollars are withdrawn at a rate of r%, find a formula for the present value of the perpetuity. Be sure to simplify your formula as much as possible. (b) Suppose P₁ is the present value of an annuity whose compounding term corresponds with the withdrawal term. Let P2 denote the present value of the situation described above, wherein the investment compounds twice for every withdrawal term. Which number should be larger, P₁ or P₂? Justify your response. (c) Suppose a $5000 annual scholarship is to be established. The Office of Advancement figures it can get an APR of 3% compounding semi-annually on any funds invested to support the scholarship. Determine the amount which must be invested today to support the fund.
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