8. Solve the following word problems, write all your answers in complete sentence and include appropriate units a) You need to ask for a loan to buy a car. The two banks that you approached offer you the following plans Bank A: 13.2% interest compounded semiannually Bank B: 12.9% interest compounded monthly Which loan would be a better deal? Bank A has and APY of 13.64% and bank B has an APY of 13.69%. Bank A is a better deal for a loan b) Find the APY for money invested at 96% compounded semiannually, 9.5% compounded weekly, and 9% compounded continuously. What would be the best investment? APY in each case is 9.83%, 9.96%, and 9.41%. Best deal for an investment is 9.5% compounded weekly c) A couple of new parents deposits $10,000 in a certicate of deposit the day their daughter is born. 1fthe account pays 4.5% compounded continuously, how much money will there be in the account the day that the daughter turns 18 years old? $22,479 d) What is the annual interest rate if an investment of $5,000 compounded monthly doubles it's value in 6 years? 1 1.6% e) A family has a half-million dollars, 30 year mortgage at 6.1% compounded monthly. Find the monthly payment. How much interest would they have paid by the time they amortize their loan. PMT = $3,029.97 I = $590,789.20 f) Parents have set up a sinking fund in order to have $120,000 in 15 years for their children's college education. How much should be paid semiannually into an account paying 4.8% compounded semiannually? $2,777 g) Eiloan recently offered 367month auto loans at 0.21% monthly rate to applicants with fair credit ratings. If you have a fair credit rating and can afford monthly payments of $350, how much can you borrow from Eloan? What is the total interest that you will pay for this loan? $12,123.25 1= $477 h) If you buy a computer directly from the manufacturer for $2,500 and agree to repay it in 48 equal installments at 1.25% interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid? PMT = $69.58 1= $839.84 i) A family is thinking about buying a house costing $350,000. They will pay 20% down, and the rest is to be amortized over 30 years in equal monthly payments. If their mortgage has an annual interest rate of 4.4% compounded monthly, what will the monthly payments be? How much total interest will be paid over 30 years? PMT = $1,402 I = $224,720 j) Rafael makes his first $1,000 deposit into an IRA earning 4.1% compounded annually on his 24th birthday and his last $1,000 deposit on his 35th birthday (12 equal deposits in all). With no additional deposits, the money in the IRA continues to earn 4.1% interest compounded annually until Rafael retires on his 65th birthday. How much is in the IRA when he retires? How much total interest did he earn? h) A company that services vending machines considers its income as a continuous stream with an annual rate flow given byf(t) : 1209941 in thousands of dollars. Find the income from this stream over the next 10 years. What is the income produced in the last year only? (Hint: you are not investing the income in this problem) $294,505 U U4r i) A continuous income stream has an annual rate of ow of [(1) = 12,0009 (in dollars). Find the future value if the income is compounded continuously at 6% for the next 8 years. $143,368 j) Starting at age 25 you deposit $2000 a year into an IRA account. Treat the yearly deposits into the account as a continuous stream of income. If money in the account earns 5% compounded continuously, how much will be in the account when you retire at age 65 (40 years later)? How much ofthc final amount is interest? $255,562 k) A small oil company considers the continuous pumping of oil from a well as a continuous income stream with annual rate of ow f0) = 600903 in thousands of dollars. Find the future value of the income stream if it's compounded continuously at 10% over the next 10 years. What interest will this investment pay? $5,165,893 r=$2,571,399