Chapter 5

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Seneca College *

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Jan 9, 2024

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MyLab Questions 1. N = 18 I = 12.5 PV = 0 PMT ? CPT = 2,557.31(a) 3,239.26(b) FV = 150,000 190,000 PY = 1 CY = 1 2. N = 10 I =? CPT = 7.55% PV = 140 PMT = 0 FV = -290 PY = 1 CY = 1
Chapter 5, Problems, Pg. 157. 1, 2, 4, 10-13, 15, 26, 28, 29, 31, 33 Equivalent n- Period Effective Rate = (1 + r ) n − 1 Q1 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 = (1 +20%)^1/4 – 1 = 4.66% b. one year = (1 + 20%)^1/2 -1 = 9.55% $1,000 x 9.55% = 1,095.50 $1,095.50 x 9.55% = $1,200.12 $1,200.12 - $1,000 = $200.12/$1,000 = 20% c. one month = 0.76% Q2. Do the relevant calculations so you can indicate which you prefer: a bank account that pays 5% per year (EAR) for 3 years or Option 1 – 5% EAR for 3 Year = $1 x (1.05)^3 = $1.15763 a. an account that pays 2.5% every 6 months for 3 years? b. an account that pays 7.5% every 18 months for 3 years? c. an account that pays 0.5% per month for 3 years? a) EAR = (1 + 2.5%)^6 = $1.1597 Pick $1 N = 6 I = 2.5 PV = -1 PMT = 0 FV = 1.1597 PY CY
b) EAR = (1 + 7.5%)^2 = $1.1556 Pick $1 N = 2 I = 7.5 PV = -1 PMT = 0 FV = 1.1556 PY CY Option 1 is better c) EAR = (1 + 0.005)^36 = $1.196681 Pick $1 N = 36 I = 0.5 PV = -1 PMT = 0 FV = 1.196681 PY CY Option c is better Q4. 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.) FORMULA for EAR = (1 + APR/m)^m - 1 A) 10% APR = (1 + 10%/12)^12 -1 = 10.47% EAR B) 10% APR = 10% EAR C) 9% APR = (1 + .09/365)^365 -1 = 9.416214% ICONV = NOM (Nominal rate, APR) 9% = EFF (Effective Rate) CPT = 9.416214% = C/Y (Compounds per year) 365 In Casio = Hit Menu, find TVM, hit a, you will see conversion, input nominal rate, Q10. Suppose for its deposit accounts Simplii Financial is offering to pay interest at a rate of 0.25% per month with monthly compounding, but Tangerine is offering to pay interest at a rate of 0.75% per
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quarter with quarterly compounding. (One quarter is equal to three months.) Which financial institution is offering the higher rate? Simplii = (1 + 0.25%) ^3 – 1 = 0.75187% (quarterly compound rate) Simplii = (1 + 0.25%) ^12 – 1 = 3.0416% EAR Tangerine = (1 + 0.75%) ^4 – 1 = 3.0339% EAR 11. You make monthly payments on your car loan. It has a quoted APR of 5% (monthly compounding). What percentage of the outstanding principal do you pay in interest each month? What is the effective monthly rate? 5%/12 = 0.4166666 12. Excel Project Suppose Capital One is advertising a 60-month, 5.99% APR motorcycle loan. If you need to borrow $8000 to purchase your dream Harley-Davidson, what will your monthly payment be? Book N = 60 I = 5.99%/12 = 0.499167 PV = 8,000 PMT = CPT = -154.62 FV = 0 Alternative N = 60 I = 5.99 PV = 8,000 PMT = CPT = -154.62 FV = 0 PY = 12 CY = 12
Q13. Suppose your friend tells you that the Bank of Montreal is offering a 30-year mortgage and your friend has converted the mortgage’s rate to the equivalent EAR of 6.80%. If you plan to borrow $150,000, what will your monthly payment be? Book (we want the APR) N = 30 x 12 = 360 I = (1 + 6.8%)^1/12 -1 = . 549737 PV = 150000 PMT = CPT =-$957.63 FV = 0 Alternative N = 360 I = ICONV = EFF 6.8, C/Y = 12, NOM or APR = 6.5968 PV = 150000 PMT = CPT = -$957.63 FV = 0 PY = 12 CY = 12 15. You have just sold your house for $1,000,000 in cash. Your mortgage was originally a 30-year mortgage with monthly payments and an initial balance of $800,000. The mortgage is currently exactly 18.5 years old, and you have just made a payment. If the interest rate on the mortgage is 7.75% (APR with semi-annual compounding), how much cash will you have from the sale once you pay off the mortgage? N = 30 x 12 = 360 I = 7.75 PV = 800,000 PMT = CPT = $5,663.87 FV = 0 PY = 12 CY = 2 N = 30 x 12 = 360 I = 7.75………..7.75/2 = 3.875% (1 + 3.875%)^1/6 -1 = PV = 800,000 PMT = CPT = $5,663.87 FV = 0 PY = 1 CY = 1 We’ve been told that we have been making monthly payments for 18.5….12 x 18.5 = 222 payments. Therefore we have 360 – 222 = 138 payments remaining. N = 138 I = 7.75
PV = CPT = $519,382.01 PMT = $5,663.87 FV = 0 PY = 12 CY = 2 Sell for $1 mill - $519,382.01 = $480,618 Q26. Excel Project You have credit card debt of $25,000 that has an APR (monthly compounding) of 15%. Each month you pay a minimum monthly payment only. You are required to pay only the outstanding interest. You have received an offer in the mail for an otherwise identical credit card with an APR of 12%. After considering all your alternatives, you decide to switch cards, roll over the outstanding balance on the old card into the new card, and borrow additional money as well. How much can you borrow today on the new card without changing the minimum monthly payment you will be required to pay? $25,000 x 15%/12 = $312.50 Change the rate to 12% ..... 12%/12 = 1% Therefore, $312.50/1% = $31,250 $31,250 x 12%/12 = $312.50 Q28 Excel Project In 1974, the interest rate was 7.782% and the rate of inflation was 12.299% in Canada. What was the real interest rate in 1974? How would the purchasing power of your savings have changed over the year? R = (nom – i)/(1 + i) = (0.0782 - .12299)/(1 + .12299) = -4.02297616% Q29. If the rate of inflation is 5%, what nominal interest rate is necessary for you to earn a 3% real interest rate on your investment? nom = 1.03 x 1.05 -1 = 8.15% Q33. You are thinking about investing $5000 in your friend’s landscaping business. Even though you know the investment is risky and you can’t be sure of the outcome, you expect your investment to be
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worth $5750 next year. You notice that the rate for one-year treasury bills is 1%. However, you feel that other investments of equal risk to your friend’s landscape business offer a 10% expected return for the year. What should you do? $5750/(1.1) = $5227.2 $5000 x 1.1 = $5500.00…invest with your friend