Question

please answer all of the following questions

31. Today is your 30 birthday and you have a dream of retiring on your 65 birthday. You want to put aside however much is necessary on your 31" through 65" birthdays (35 annual payments) to have enough to retire. You've estimated that you will live until you are 90 and you want the first withdrawal to occur on your 66° birthday, with the last payment occurring on your 90 birthday. You think that you will need $150,000 per year to spend during retirement. You estimate constant interest rates of 11.25%. Assuming that you currently have $7,500 deposited in your retirement account, how much must you put aside each year in order to have sufficient money to retire at age 652 32. Daigo Dojima recently invested $7,500 in a project that is promising to return 6.25 percent per year. The cash flows are expected to be as follows: End of Cash Year Flow $1000 950 875 Y? 850 Note that the 4 year cash flow is unknown. Assuming the present value of this cash flow stream is $7,500 (that is, CFO -7500), what is the missing cash flow value (that is, what is the cash flow at the end of the 4th year)? 33. Assume that you have a $22,500 balance on your credit card. You plan to make monthly payments of $450 until the balance is paid off. The interest rate on your credit card is 17.5% p.a. compounded monthly. A letter in the mail informs you that you are approved for a new credit card and balance transfers are subject to a 9.5% p.a., compounded monthly. How many months sooner will you pay off your bill?

Answer 1

31). Number of years of retirement = 90 -65 = 25.

Total funds needed at the 66th birthday = 25*amount needed per year = 25*150,000 = 3,750,000

Last deposit will be made on the 65th birthday, so the target amount needed then will be 3,750,000/(1+11.25%) = 3,370,786.50

Annual deposits calculation: PV = 7,500; FV = -3,370,786.50; N = 35; rate = 11.25%, solve for PMT

Annual deposits required = 8,444.81

32). Initial cash outlay = sum of present values of cash outflows discounted at the internal rate of return

7,500 = 1,000/(1+6.25%) + 950/(1+6.25)^2 + 875/(1+6.25%)^3 + CF4/(1+6.25%)^4 + 850/(1+6.25%)^5

CF4 = 4,360.08*(1+6.25%)^4 = 5,661.94

33). Number of payments to be made if interest rate is 17.5% p.a.: PV = 22,500; PMT = -450; rate = 17.5%/12 = 1.46%, solve for Nper.

Number of payments = 90.22 or 91 (rounded to the next payment)

If the monthly payment remains same at 450 but interest rate is now 9.5% p.a. then number of payments to be made is:

PV = 22,500; PMT = -450; rate = 0.79%, solve for Nper.

Number of payments = 63.90 or 64 (rounded to the next payment)

Difference in the number of payments = 91 - 64 = 27 months.

The debt will be paid off, by 27 months sooner.