5. 4. You possess schemet three bombardment exquisites for a one-year pawn: 10% APR Compounded monthly, 10% APR compounded year-by-year, and 9% APR compounded daily. Compute the EAR for each bombardment exquisite. (Assume that there are 365 days in the year. ) Sol: 1+EAR= (1+r/k)k So, for 10% APR compounded monthly, the EAR is 1+EAR= (1+0. 1/12)12 = 1. 10471 => EAR= 10. 47% For 10% compounded year-by-year, the EAR is 1+EAR= (1+0. 1)=1. 1 * EAR= 10% (recrement the selfsame). For 9% compounded daily 1+EAR= (1+0. 09/365)365 = 1. 09416 * EAR= 9. 4% 5-8. You can gain $50 in attention on a $1000 pawn for eight months.
If the EAR is the selfselfsame unobservant of the protraction of the bombardment, how plenteous attention win you gain on a $1000 pawn for a. 6 months. b. 1 year. c. 1 1/2 years. Sol: Since we can gain $50 attention on a $1000 pawn, Reprimand of attention is 5% Therefore, EAR = (1. 05)12/8 -1 =7. 593% a) 1000(1. 075936/12 – 1) = 37. 27 b) 1000(1. 07593? 1) = 75. 93 c) 1000(1. 075933/2 ? 1) = 116. 03 5-12. Capital One is advertising a 60-month, 5. 99% APR motorcycle advance. If you scarcity to attribute $8000 to escheatment your romance Harley Davidson, what win your monthly reimbursement be? Sol: Remittance reprimand for 12 months is, 5. 99/12 = 0. 499167%
C= 8000/[1/0. 004991(1-1/(1+0. 004991)60)] = $154. 63 5-16. You possess sound escheatmentd a abode and fascinated out a $500,000 advance. The advance has a 30-year order behind a while monthly reimbursements and an APR of 6%. a. How plenteous win you pay in attention, and how plenteous win you pay in prominent, during the leading year? b. How plenteous win you pay in attention, and how plenteous win you pay in prominent, during the 20th year (i. e. , among 19 and 20 years from now)? Sol: a. APR of 6%/12 = 0. 5% per month. Reimbursement = 500,000/[(1/. 005)(1- 1/1. 005360)]= $2997. 75 Total annual reimbursements = 2997. 75 ? 12 = $35,973. Advance Et behind 1 year is 2997. 5[1/0. 005(1- 1/1. 005348)] = $493,860. Therefore, 500,000 – 493,860 = $6140 is prominent repaid in leading year. Attention paid in 1st year is 35,973 – 6140 = $29833. b. Advance et in 19 years (or 360 – 19? 12 = 132 fostering pmts) is 2997. 75[1/0. 005(1- 1/1. 005192)]= $289,162 Advance Et in 20 years = 2997. 75[1/0. 005(1- 1/1. 005120)] = $270,018 Therefore, Prominent repaid = 289,162 – 270,018 = $19,144, and Attention repaid =$35,973 – 19,144 = $16,829. 5-20. Oppenheimer Bank is presenting a 30-year advance behind a while an APR of 5. 25%. Behind a while this advance your monthly reimbursements would be $2000 per month.
In union, Oppenheimer Bank presents you the succeedingcited deal: Instead of making the monthly reimbursement of $2000 integral month, you can execute half the reimbursement integral two weeks (so that you win execute 52 ? 2 = 26 reimbursements per year). Behind a while this scheme, how desire win it capture to pay off the advance of $150,000 if the EAR of the advance is illegal? Sol: For integral 2 weeks reimbursement = 2000/2 = 1000. 1 year = 26 weeks. Therefore, (1. 0525)1/26 = 1. 001970. So, remittance reprimand = 0. 1970%. Here, PV of advance reimbursements is the uncollected et. 150, 000= (1000/0. 001970)[1- 1/(1. 001970)N] If we explain for N,
We get N= 177. 98. So, it captures 178 months to pay off the advance. If we determine to pay for 2 weeks, then 178*2= 356 weeks. 5-24. You possess confidence card liability of $25,000 that has an APR (monthly compounding) of 15%. Each month you pay the restriction monthly reimbursement simply. You are required to pay simply the uncollected attention. You possess accepted an present in the mail for an inadequately same confidence card behind a while an APR of 12%. Behind because all your alternatives, you determine to switch cards, roll pit the uncollected et on the old card into the new card, and attribute unional money as courteous.
How plenteous can you attribute today on the new card behind a whileout changing the restriction monthly reimbursement you win be required to pay? Sol: Here the remittance reprimand = 15/12 = 1. 25%. Assuming that monthly reimbursement is the attention we get, 25,000*0. 15/12= $312. 50. This is permanence. So the total can be attributeed at the new attention reprimand is this capital career remittanceed at the new remittance reprimand. The new remittance reprimand is 12/12 = 1%. So, PV = 312. 50/0. 01 = $31,250. So by switching confidence cards we are efficacious to expend an extra 31, 250 ? 25, 000 = $6, 250. We do not possess to pay taxes on this total of new attributeing, so this is our behind-tax utility of switching cards. -28. Consider a purpose that requires an modereprove bombardment of $100,000 and win product a uncombined capital career of $150,000 in five years. a. What is the NPV of this purpose if the five-year attention reprimand is 5% (EAR)? b. What is the NPV of this purpose if the five-year attention reprimand is 10% (EAR)? c. What is the main five-year attention reprimand such that this purpose is stationary useful? Sol: a. NPV = –100,000 + 150,000 / 1. 055 = $17,529. b. NPV = –100,000 + 150,000 / 1. 105 = –$6862. Here we scarcity to investigate the IRR. Therefore, IRR = (150,000 / 100,000)1/5 – 1 = 8. 45%. 5-32. Suppose the general one-year attention reprimand is 6%.
One year from now, you consider the rule win begin to slack and the one-year attention reprimand win descend to 5%. In two years, you look-for the rule to be in the throng of a recession, causing the Federal Reserve to cut attention reprimands drastically and the one-year attention reprimand to descend to 2%. The one-year attention reprimand win then mollify to 3% the succeedingcited year, and live to mollify by 1% per year until it receipts to 6%, where it win halt from then on. a. If you were real respecting these coming attention reprimand changes, what two-year attention reprimand would be congruous behind a while these look-forations? . What general order erection of attention reprimands, for orders of 1 to 10 years, would be congruous behind a while these look-forations? c. Plot the resign deflexion in this plight. How does the one-year attention reprimand assimilate to the 10-year attention reprimand? Sol: a. The one-year attention reprimand is 6%. If reprimands descend direct year to 5%, then if you reinvest at this reprimand pit two years you would gain (1. 06)(1. 05) = 1. 113 per dollar invested. This total corresponds to an EAR of (1. 113)1/2 – 1 = 5. 50% per year for two years. Thus, the two-year reprimand that is congruous behind a while these look-forations is 5. 0%. b. Year| Coming Attention Rate| FV from re-investing| EAR| 1| 6%| 1. 0600| 6. 00%| 2| 5%| 1. 1130| 5. 50%| 3| 2%| 1. 1353| 4. 32%| 4| 3%| 1. 1693| 3. 99%| 5| 4%| 1. 2161 | 3. 99%| 6| 5%| 1. 2769 | 4. 16%| 7| 6%| 1. 3535 | 4. 42%| 8| 6%| 1. 4347 | 4. 62%| 9| 6%| 1. 5208 | 4. 77%| 10| 6%| 1. 6121 | 4. 89%| c. We can get the resign deflexion by because all EARs balancehead. It is an inverted deflexion. 5-36. You are enrolling in an MBA program. To pay your schooling, you can either capture out a scale novice advance (so the attention reimbursements are not tax deductible) behind a while an EAR of 5 ? or you can use a tax-deductible abode equity advance behind a while an APR (monthly) of 6%. You prepare nature in a very low tax unite, so your tax reprimand win be simply 15%. Which advance should you use? Sol: APR is abandoned, So we can get EAR by, (1+0. 06/12)12 = 1. 06168. So, EAR = 6. 168%. We possess to apply the anteriorly tax reprimand to behind tax reprimand. 6. 168? (1- 0. 15) = 5. 243% Since novice advance is excellent behind tax reprimand, it is melioreprove to use abode equity advance. 5-40. You determined is because the escheatment of a new employment phone method. You can either pay $32,000 now, or $1000 per month for 36 months. . Suppose your determined generally attributes at a reprimand of 6% per year (APR behind a while monthly compounding). Which reimbursement scheme is balance engaging? b. Suppose your determined generally attributes at a reprimand of 18% per year (APR behind a while monthly compounding). Which reimbursement scheme would be balance engaging in this plight? Sol: a. The reimbursements are as foolhardy as the determined’s other liability. So, convenience consume = liability reprimand. PV(36 month annuity of 1000 at 6%/12 per month) = $32,871. So we scarcity to pay capital. b. PV(annuity at 18%/12 per months) = $27,661. So we can pay pit span.