Explanation Given Information: I want to establish a trust fund from which my heirs can withdraw $2000 per month for 20 years. The following table shows the average return for some of the largest mutual funds commonly found in the retirement account: Mutual Fund Fidelity Growth company Vanguard 500 Index PIMCO Total Return Vanguard Total Bond Market Index Rate of return 14.83 % 13.25 % 2.77 % 2.67 % Type Stock fund Stock fund Bond fund Bond fund Formula used: Suppose one’s has an account with an interest rate of i per compounding period. If one’s receive a payment of PMT at the end of the compounding period, and the account is down to zero after n periods, then the starting balance of the account is given by: P V = P M T 1 − ( 1 + i ) − n i Calculation: Consider the provided information that one will want to establish a trust fund from which one’s heirs can withdraw $2000 per month for 20 years. Since, the amount funded is $2,000, Hence, P M T = 2 , 000 Also, since they are funded for a period of 20 years, so, in order to convert it into months, multiply by 12. n = 20 × 12 = 240 According to the table, the return rate for Vanguard fund is 13.25 % per year. Hence, i is given by: 13.25 % = 13.25 100 = 0.1325 Since, there are 12 periods, interest per period is: i = 0.1325 12 The starting balance of the account is given by: P V = P M T 1 − ( 1 + i ) − n i Substitute 2,000 for PMT , 240 for n and 0.1325 12 for i in P V = P M T 1 − ( 1 + i ) − n i . P V = 2 , 000 [ 1 − ( 1 + 0.1325 / 12 ) − 240 0.1325 / 12 ] Use TI83 calculator and steps of calculator is shown below; Step 1: Press the ON key

7th Edition

ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 2.3, Problem 54E

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To calculate: What should be the amount of fund if I invest in Vanguard stock fund and the amount, my heirs will receive is $100,000, so that they can withdrawal $2000 per month for 20 years.

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Chapter 2.3, Problem 53E

Chapter 2.3, Problem 55E

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What should be the amount of fund if I invest in Vanguard stock fund and the amount, my heirs will receive is $100,000, so that they can withdrawal $2000 per month for 20 years.

Solution Summary: The author calculates the amount of a trust fund from which one's heirs can withdraw 2000 per month for 20 years.

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To calculate: What should be the amount of fund if I invest in Vanguard stock fund and the amount, my heirs will receive is $100,000, so that they can withdrawal $2000 per month for 20 years.

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