An alumnus has donated $4,000,000 to the Poole College of Management. The College plans to invest this donation in an account earning 10% compounded annually for at least five years before it starts to use the donation for student scholarships.

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App C Graded Assignment Note: The factor tables are at the back of the textbook. The same tables are also available in the App C Moodle block. Reminder: To receive partial credit on problems which require calculations, the calculations must be shown. Problem I: (12 pts) If a company invests $10,000 today at 8% interest for four years, indicate in the table below the \"n\" and \"i\" combinations that should be used to solve for the future value. If interest is compounded: Total number of compounding periods Interest rate per compounding period \"n\" \"i\" or \"r\" Annually Semi-annually Quarterly Problem II: (15 pts) An alumnus has donated $4,000,000 to the Poole College of Management. The College plans to invest this donation in an account earning 10% compounded annually for at least five years before it starts to use the donation for student scholarships. A. Rounded to the nearest whole dollar, if the College does not make any withdrawals from its investment account, what will be the future value of this investment in five years? Answer: $ B. By comparing your answer above to the amount originally invested, calculate the amount of total interest the donated amount will earn over five years. Answer: $ C. If the College would like the future value of the donation to equal $7,369,760 in five years, what interest rate compounded annually would it need to earn? Answer: __ % 1 Problem III: (20 pts) On 1/1/20X0, Nicholas makes a new year's resolution to start saving for a mountain climbing vacation he plans to take in four years. Beginning in one year (1/1/20X1), he plans to invest $2,000 per year for 4 years in an investment with an annual return of 7% compounded annually. A. Rounded to the nearest whole dollar, how much will be in his investment account on 1/1/20X4, the date of his last investment? Answer: $ B. How much total interest was earned over the life of his $2,000 investments? Answer: $ C. Below is a partial amortization schedule for the vacation fund. Rounding to the nearest whole dollar, fill in all the missing spaces (gray blocks). Date 1/1/20X1 1/1/20X2 1/1/20X3 1/1/20X4 Total Annual Cash Savings 2,000 2,000 2,000 2,000 8,000 Interest Revenue ---140 Accumulated Balance 2,000 4,140 D. Accounting Check Does the amortization schedule's accumulated balance at 1/1/20X4 match your answer to part \"A\" and does the total interest revenue amount match your answer to part \"B\"? If your answer is not \"yes\" to both questions, please go back and check your work. E. What kind of pattern over time do you notice with respect to interest revenue and the accumulated balance? (one sentence) 2 Problem IV: (23 pts)On 1/1/X1, Mercury Corp. takes out a loan for $20,000 to purchase equipment for its manufacturing facility. The loan will be repaid in equal semi-annual installments over 2 years beginning 6/30/X1. The interest rate on the loan is 12% compounded semi-annually. A. Rounded to the nearest whole dollar, how much will each semi-annual installment be? Answer: $ B. How much total interest will be paid over the life of the loan? Answer: $ C. Below is a partial amortization schedule for the equipment loan. Rounding to the nearest whole dollar, fill in all the missing spaces (gray blocks). Date 1/1/20X1 1/1/20X2 1/1/20X3 1/1/20X4 1/1/20X5 Total Semi-Annual Cash Payment ---- Interest Expense ---- Accumulated Balance 20,000 15,428 D. Accounting Check Since each loan payment is a payment towards principal and interest, does the amortization schedule's accumulated balance at 1/1/20X5 equal zero? Does the total interest expense amount match your answer to part \"B\"? If your answer is not \"yes\" to both questions, please go back and check your work. E. What kind of pattern over time do you notice with respect to interest expense and the accumulated balance? (one sentence) 3 Problem V: (15 pts) Jorge has just received a $2,000,000 payout for winning a local lottery. He plans to immediately retire from his full-time job and live completely off of his winnings. He plans to invest his winnings in an investment account earning 12% compounded annually. Jorge has determined that he will need to withdraw $255,000 from his account at the end of each year in order to have the lifestyle he wants. A. How many years will Jorge be able to withdraw this annual amount before he has depleted his inheritance? Answer: ___ years B. Intuitively, if Jorge earns 10% compounded annually on his inheritance instead of 12% but still withdraws the same amount annually, will he run out of money sooner or later than in your answer to part \"A\"? (one sentence) C. Approximately, how many years will Jorge be able to withdraw $255,000 each year before he runs out of money if his investment account is earning 10% compounded annually? Answer: between _______ years Problem VI: (15 pts) Pamela, a recent graduate from NC State, would like to have $20,000 saved in five years in order to make a down payment on her first house. She believes that given her tolerance for risk, she can earn 12% on any savings she has. A. Rounded to the nearest whole dollar, how much would Pamela need to set aside today in order to achieve her goal if she can earn 12% compounded annually? Round to the nearest penny. Answer: $ B. Rounded to the nearest whole dollar, how much would Pamela need to set aside today in a single lump-sum amount in order to achieve her goal if she can earn 12% compounded quarterly? Answer: $ C. Referring to your answers for \"A\" and \"B\