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May deposits PhP 20,000 into a fund at the beginning of nd of 15 years, she makes an additional deposit of X. nd of 20 years, May uses the accumulated balance in the fu te with annual payments of PhP 30,000 per year for 10 thereafter. is credited at an annual effective rate of 6%. Calculate X

May deposits PhP 20,000 into a fund at the beginning of nd of 15 years, she makes an additional deposit of X. nd of 20 years, May uses the accumulated balance in the fu te with annual payments of PhP 30,000 per year for 10 thereafter. is credited at an annual effective rate of 6%. Calculate X

Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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Find X, the deposit at the end of 15 years. Use the perpetuities for this question that is given on the second photo
2.4 Perpetuities A perpetuity is an annuity in which the payments continue forever, i.e., the term of the annuity is not finite. The following are examples of perpetuities: • Dividends on preferred stock with no redemption provision. • British consols, which are nonredeemable obligations of the British government. We use the following notations to denote perpetuities: 1 • perpetuity-immediate: a = 1 • perpetuity-due: äö| d Example 6. Deposits of 1000 are placed into a fund at the beginning of each year for the next 20 years. After this, the fund will give annual payments at the end of each year starting from the 30th year and continue forever. Find an expression for the amount of payments. Solution: The deposits and payments are illustrated below: 1000 1000 1000 deposits 0 1 19 20 29 30 31 ... P payments To solve this problem, we may value all amounts at time 0. You may also value the payments at other time periods. Hence, 1000äm = Pv29 a. Solving for P and using the formulas for the terms in the equation, we get P = (1+ i)30 – (1+i)10.
Transcribed Image Text:2.4 Perpetuities A perpetuity is an annuity in which the payments continue forever, i.e., the term of the annuity is not finite. The following are examples of perpetuities: • Dividends on preferred stock with no redemption provision. • British consols, which are nonredeemable obligations of the British government. We use the following notations to denote perpetuities: 1 • perpetuity-immediate: a = 1 • perpetuity-due: äö| d Example 6. Deposits of 1000 are placed into a fund at the beginning of each year for the next 20 years. After this, the fund will give annual payments at the end of each year starting from the 30th year and continue forever. Find an expression for the amount of payments. Solution: The deposits and payments are illustrated below: 1000 1000 1000 deposits 0 1 19 20 29 30 31 ... P payments To solve this problem, we may value all amounts at time 0. You may also value the payments at other time periods. Hence, 1000äm = Pv29 a. Solving for P and using the formulas for the terms in the equation, we get P = (1+ i)30 – (1+i)10.
1 May deposits PhP 20,000 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, May uses the accumulated balance in the fund to buy a perpetuity- immediate with annual payments of PhP 30,000 per year for 10 years, and PhP 15,000 per year thereafter. Interest is credited at an annual effective rate of 6%. Calculate X.
Transcribed Image Text:1 May deposits PhP 20,000 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, May uses the accumulated balance in the fund to buy a perpetuity- immediate with annual payments of PhP 30,000 per year for 10 years, and PhP 15,000 per year thereafter. Interest is credited at an annual effective rate of 6%. Calculate X.
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