Part (a) Compute the amount that a $20,000 investment today would accumulate at
ID: 2356811 • Letter: P
Question
Part (a) Compute the amount that a $20,000 investment today would accumulate at 10% (compound interest) by the end of 6 years. Part (b) Tom wants to retire at the end of this year (2010). His life expectancy is 20 years from his retirement. Tom has come to you, his CPA, to learn how much he should deposit on December 31, 2010 to be able to withdraw $40,000 at the end of each year for the next 20 years, assuming the amount on deposit will earn 8% interest annually. Part (c) Cathy P. Value has a $1,200 overdue debt for intermediate accounting books and supplies at HPU's Bookstore. She has only $400 in her checking account and doesn't want her parents to know about this debt. The bookstore manager tells her that she may settle the account in one of two ways since she can't pay it all now: 1. Pay $400 now and $1,000 when she completes her degree, two years from today. 2. Pay $1,600 one year after completion of her degree, three years from today. Assuming that the cost of money is the only factor in Cathy's decision and that the cost of money to her is 8%, which alternative should she choose? Your answer must be supported with calculations.Explanation / Answer
a. FV =PV*(1+i)^n = 20000*(1+10%)^6 = $35,431.22 b. ANnual Payment reqd = PMT = 40,000 Term = nper = 20 ys Ianterest = Rate = 8% So PV of this annuity = PV(Rate,nper,PMT) = PV(8%,20,40000) = $392,725.90 c. Int rate i = 8% Option 1: Pay $400 now. SO remaining debt = 1200-400 = 800 (PV). So After 2 yrs, yu pay $1000 (FV). SO Cathy is paying 1000-800 = 200 as Int for 2 Yrs on $800 We know FV = PV*(1+i)^n ie (1+i)^n = FV/PV = 1000/800 = 1.25 ie nLog (1+i) = Log 1.25 ie Log (1+i) = (1/2)*Log1.25 ie (1+i) = 1.25^(1/2) = 1.12 so i = 0.12 or 12% Option 2: Pay 1600 (FV) after 3 yrs. PV = 1200 So We know FV = PV*(1+i)^n ie (1+i)^n = FV/PV = 1600/1200 = 1.33 ie nLog (1+i) = Log 1.33 ie Log (1+i) = (1/3)*Log1.33 ie (1+i) = 1.33^(1/3)= 1.10 So i = 10% SO Cathy should take Option 2 as Int is 10% which is less than 12% and is closeer to her 8% limit