Assignment 6

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Loyalist College *

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Finance

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Apr 3, 2024

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docx

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Assignment # 6 1. Your bank is offering you an account that will pay 20% interest in total for a two-year deposit. Determine the equivalent discount rate for a period length of a. six months. b. one year. c. one month. a) 6/24 = ¼ r= ((1+.20)-1)^1-4-1 = (1.20)^0.25 -1 = 1.0466 – 1 =0.0466 = 4.66% b) ½ r = ((1+.20)/1)^1/2-1 = (1.20)^0.5 -1 = 0.0954 = 9.54% c)1/24 r= ((1+.20)/1)^1/24-1 =(1.20)0.041-1 =1.0075-1 =0.0075 =.075% 2. Excel Project You have found three investment choices for a one-year deposit: 10% APR compounded monthly, 10% APR compounded annually, and 9% APR compounded daily. Compute the EAR for each investment choice. (Assume that there are 365 days in the year) For an account with 10% APR with monthly compounding you will have: EAR = (1+0.10/12)^12-1 = 10.47% For an account with 10% APR with annual compounding you will have: EAR = (1+.01)^1 -1= 10% For an account with 9% APR with daily compounding you will have: EAR = (1+.09/365)^365 -1 = 9.42% 3. Excel Solution You have been accepted into university. The university guarantees that your tuition will not increase for the four years you attend. The first $10,000 tuition payment is due in six months. After that, the same payment is due every six months until you have made a total of eight payments. The university offers a bank account that allows you to withdraw money every six months and has a fixed APR of 4% (semi-annual) guaranteed to remain the same over the next four years. How much money must you deposit today if you intend to make no further deposits and would like to make all the tuition payments from this account, leaving the account empty when the last payment is made r=0.04/2 = 0.02
PV Annuity = PMT x (1/r) x (1-(1/1+r)^n) PV Annuity = 10,000 x (1/0.02) x (1-(1/1.02)^8) PV Annuity = $73,254.61 4. You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is $2356, and you have made every payment on time. The original term of the mortgage was 30 years, and the mortgage is exactly 4 years and 8 months old. You have just made your monthly payment. The mortgage interest rate is 6.2% (APR with semi-annual compounding). How much do you owe on the mortgage today Timeline 56 57 58 360 0 1 2 304 2356 2356 2356 Discount rate = 6.2/12 = 0.5167 So PV = 2,356/0.005167((1-1/1.005167)^34) =$376,905.28 5. You have some extra cash this month and are considering putting it toward your car loan. Your interest rate is 7%, your loan payments are $600 per month, and you have 36 months left on your loan. If you pay an additional $1000 with your next regular $600 payment (due in one month), how much will it reduce the amount of time left to pay off your loan? Loan Balance = PV Annuity = PMT x (1/r) x (1-(1/(1+r)^n) PV = 600 (1/0.00583333)(1-(1/1+0.00583333)^36)=19431.88 Loan Balance After 1000 PMT = 19431.88 (1+0.00583333) -1000-600 = 17945.23 Months Left = NPER (0.00583333,-600,17945.23) = 32.96 = 33 Months
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