Chapter 3 problem sets and quiz- If your bank pays you 1.4% interest and you pay deposit $850 today, what will be your balance in seven years? N=7, I/Y=1.4, PV=850, PMT=0,FV=$936.88- You plan to borrow $3000 from a bank. In exchange for $3000 today, you promise to pay $3210 in one year. What does the cash flow timeline look like from your perspective? What does it look like from the bank’s perspective? Your perspective (+3000, -3000) bank’s perspective (-3000,+3000)- Your brother has offered to give you either $5000 today or $10000 in 11 years. If the interest rate is 4% per year, which option is preferable? N=11, I/Y=4, PV=$6496.81, PMT=0, FV=10000. Take the future amount because it is greater than the amount offered today.- Your grandfather put some money into an account for you on the day you were born. You are now 18 years old and are allowed to withdraw the money. The account currently has $3996 in it and pays an 8% interest rate. 25th birthday: N=7 (25-18), I/Y=8, PV=3996, PMT=0, FV=$6848.44>>65th birthday: N=47 (65-18), I/Y=8, PV=3996, PMT=0, FV=$148779.12>>Original amount: N=18, I/Y=8, PV=3996, PMT=0, FV=$1000- The local electronics store is offering a promotion 1 year same as cash, meaning that you can buy a TV now, and wait a year to pay (with no interest). So, if you take home a $1000 TV today, you will owe them $1000 in one year. If your bank is offering you 4% interest, what is the truecost of the TV to you today? N=1, I/Y=4, PV=$961.54, PMT=0, FV=1000- Suppose Big Bank offers an interest rate of 8.0% on both savings and loans, and Bank Enn offers an interest rate of 8.5% on both savings and loans. What profit opportunity is available? Take a loan form Big Bank at 8.0% and save the money in Bank Enn at 8.5%. Surge in demand and surge in deposits? Big Bank would experience a surge in demand for loans, while Bank Enn receives surge in deposits. Interest rate? Big Bank would increase its interest rate and Bank Enn would decrease its rate.- Suppose the interest rate is 4.0%. $200 today in one year? N=1, I/Y=4, PV=200, PMT=0, FV=$208.00. $200 in one year today? 200 / (1+.04)=$192.31. TRUE- You just won a prize that comes with two payout choices. The first option is to get $120000 right now and nothing hereafter. The second option is to get $96000 right now and $10000 three years from now (and nothing after that). If you discount rate is 9%, which should you take? First option - Your cousin is currently 14 years old. She will be going to college in 4 years. Your aunt and uncle would like to have $105000 in a savings account to fund for her education at that time. If the account promises to pay a fixed interest rate of 3.6% per year. How much money do they need to put into the account today to ensure that they will have $105000 in 4 years? N=4, I/Y=3.6, PV=$91148.66, PMT=0, FV=105000- Suppose you invest $900 in an account paying 8% interest per year. What is the balance in the account after 2 years? How much of this balance corresponds interest on interest? The balance after 2 years $900×(1+0.08)2=$1049.76 Interest on interest $900×0.08×2+900=$1044.00 1049.76-1044.00=$5.76 What is the balance account after 34 years? 900×(1+0.08)34=$12321.12 900×0.08×34+900=$3348.00 Interest on interest 12321.12-3348.00=$8973.12- You expect to have $1000 in one year. A bank is offering loans at 6.0%. How much can you borrow today? 1000÷1.0.06=$943.40- What is the present value of $14000 received: 24 years from today when the interest rate is 10% per year? 14000÷(1.10)24=$1421 12 years fromtoday when the interest rate is 10% per year? 14000÷(1.10)12=$4461 6 years from today when the interest rate is 10% per year? 14000÷(1.10)6=$7903- You are planning to invest $2,000 in an account earning 5% per year for retirement. If you put the $2000 in an account at age 23, and withdraw it 33 years later, how much will you have? 20000×(1+0.05)33=10006.38 if you wait 10 years before making the deposit, so that it stays in the account for only 23 years, how much will you have at the end? 20000×(1+0.05)23=6143.05Chapter 4 and 5 problem set and quiz- You figure that the total cost of college will be $100,000 per year for 18 years from today. If your discount rate is 8% compounded annually, what is the present value today of four years of college costs starting 18 years from today? 100,000÷1.0818+100,000÷1.0819+100,000÷1.0820+100,000÷1.0821=$89,517 (nearest dollar)- You are considering two ways of financing a spring break vacation. You could put it on your credit card, at 15% APR, compounded monthly, or borrow the money from your parents, who wants an interest payment of 8% every six months. Which is the lower rate? Credit card (1+0.15÷12)12-1=16.08% loan from your parents (1+0.08)2-1=%16.64- You are thinking of building a new machine that will save you $1000 in the first year. The machine will then begin to wear out so that the savings decline at a rate of 4% per year forever. What is the present value of the savings if the interest rate is 7% per year? $1000÷(0.07-(-0.04)=$9091- You want to endow a scholarship that will pay $10000 per year forever, starting one year from now. If the school’s endowment discount rate is 7%, what amount must you donate to endow the scholarship? 10,000÷0.07=$142,857.14- Assume you graduate from college with $25000 in student loans. If your interest rate is fixed at 4.90% APR with monthly compounding and yourepay the loans over a 10-year period, what will be your monthly payment? $25,000÷[1÷0.0040833-1÷(0.0040833)(1.0040833)120=$263.94 (10)*(12)=120- Assume that Social Security promises you $35,000 per year starting when you retire 45 years from today (the first $35,000 will get paid 45 yearsfrom now). If your discount rate is 7%, compounded annually, and you plan to live for 14 years after retiring, (so that you will receive a total of 15 payments including the first one), what is the value today of Social Security’s promise? (35,000÷0.07)×(1-(1÷(1+0.07)15=$318,776.99 $318,776.99÷(1+0.07)44=$16,240.55- You have just taken out a $25000 car loan with a 7% APR, compounded monthly. The loan is for five years. When you make your first payment in one month, how much of the payment will go toward the principal of the loan and how much will go toward interest? When you make your first payment, $349.20 (495.03-145.83) will go toward the principal of the loan and $145.83 (25000×0.005833333) will go toward the interest.- You are looking to buy a