FNAN 303 Fall 2020 Quiz 2 Solutions(1).docx - Quiz 2...

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Quiz 2 Solutions Annual savings amount with annuity due to fund fixed perpetuity 1. Hope wants to establish a charitable foundation that will make annual scholarship payments of $23,000 per year forever. Hope wants the foundation to make the first annual $23,000 scholarship payment in 7 years from today and she wants scholarship payments of $23,000 per year to continue every year after that first payment. To fund the foundation, Hope plans to make equal annual donations to the foundation for 6 years. How much does Hope need to donate to the foundation each year for 6 years to have exactly enough in the foundation to make the planned annual scholarship payments if she makes her first annual donation to the foundation today, all annual donations to the foundation are equal, and funds held by the foundation are expected to earn 7.4 percent per year? A. An amount equal to or greater than $30,000 but less than $42,000 B. An amount equal to or greater than $42,000 but less than $54,000 C. An amount equal to or greater than $54,000 but less than $62,000 D. An amount equal to or greater than $62,000 but less than $70,000 E. An amount less than $30,000 or an amount equal to or greater than $70,000
Step 1: Determine how much savings needs to be accumulated to pay for the annual scholarship Step 2: Determine how much needs to be saved each year (?B) to accumulate the amount identified in step 1 Time 0 1 2 3 4 5 6 7 8 9 10 Re-time 0 1 2 3 4 Payment # 1 2 3 4 Scholarship pmt 23k 23k 23k 23k Present value ?A Time 0 1 2 3 4 5 6 7 8 9 10 Payment # 1 2 3 4 5 6 Donation pmt ?B ?B ?B ?B ?B ?B Future value ?A Step 1: Determine how much savings needs to be accumulated to pay for the annual scholarship The scholarship payments reflect a fixed perpetuity with payments of $23,000 and a discount rate of 7.4%. Therefore, the present value of this fixed perpetuity as of 6 years from now, which is 1 year before the first payment, can be found as C/r. The present value is the amount needed one year before the scholarship payments start to pay the annual scholarships of $23,000 forever. As of 6 years from today, PV 6 = C/r = 23,000 / .074 = $310,811 Hope needs to accumulate $310,811 as of 6 years from today Step 2: Determine how much needs to be saved each year (?B) to accumulate the amount identified in step 1 If Hope donates a fixed amount of money for 6 years with her first donation today and her last in 5 years from today, then the amount that she needs to save each year to accumulate $310,811 in 6 years is the annual payment associated with a 6-period annuity due with a future value of 310,811. BEGIN mode Enter 6 7.4 0 310,811 N I% PV PMT FV Solve for -40,050

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