Please provide and explanation of all anwers as well as formulas used. 6. How mu

Question

Please provide and explanation of all anwers as well as formulas used.

6. How much must I deposit today if I want to be able to withdraw $620 per month for six years from an account which earns a nominal rate of three percent, compounded monthly, if withdrawals are made at the beginning of each month? Round to the nearest cent. Do not include any unit (If your answer is $111.11, then type 111.11 without $ sign.)

7. You are establishing a fund that pays $1,000 annual scholarship to a student at Bauer Collage of Business starting a year from today, forever. If you can earn 8 percent annual return, how much do you have to put aside to keep this scholarship forever? Round to the nearest cent. Do not include any unit (If your answer is $111.11, then type 111.11 without $ sign.)

8. You just welcomed a new born boy. You want him to go to Harvard and you estimated that he will need $80,000 a year for 4 years starting 18 years from today. You are wondering how much money you need to invest in today in an investment gives 4 percent annual return to pay your son’s cost of college. How much do you need now? Round to the nearest cent. Do not include any unit (If your answer is $111.11, then type 111.11 without $ sign.)

9. Your friend brought up an investment opportunity that will generate cash flows of $5,000, $5,300, and $6,000 next three years, respectively. If your required rate of return on this investment is 12%, how much at most are you willing to pay? Round to the nearest cent. Do not include any unit (If your answer is $111.11, then type 111.11 without $ sign.)

10. What is the effective annual yield of 6% compounded quarterly? Answer in the percent format. Round to the nearest hundredth percent. Do not include any unity (If your answer is 4.36%, then enter 4.36 as your answer without % sign).

Explanation / Answer

Answer 6.

Monthly Withdrawal = $620
Period = 6 years or 72 months
Annual Interest Rate = 3%
Monthly Interest Rate = 0.25%

Present Value of Withdrawals = $620 + $620/1.0025 + $620/1.0025^2 + ... + $620/1.0025^71
Present Value of Withdrawals = $620 * 1.0025 * (1 - (1/1.0025)^72) / 0.0025
Present Value of Withdrawals = $620 * 65.9814
Present Value of Withdrawals = $40,908.47

So, you should invest $40,908.47 today

Answer 7.

Annual Payment = $1,000
Interest Rate = 8%

Present Value of Perpetuity = Annual Payment / Interest Rate
Present Value of Perpetuity = $1,000 / 0.08
Present Value of Perpetuity = $12,500

So, you should keep $12,500 aside for this scholarship

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