fin3403 ch4 hw

An ordinary annuity is set up that will pay $1500 per year for ten years. What is the present value (PV) of this annuity given that the discount rate is 7.25%? Round to the nearest whole dollar.

$10415 Pmt = 1500 N = 10 I = 7.25 PV = ? PV = 10415

Jose has the opportunity to invest in a scheme which will pay $5000 at the end of each of the next 5 years. He must invest $10,000 at the start of the first year and an additional $10,000 at the end of the first year. What is the present value of this investment if the interest rate is 8%? Round to the nearest whole dollar.

$704 Calculator CF0- -10000, CF1- -5000 (this because you invest 10,000 and get paid 5000), CF2- 5000, CF3- 5000, CF4-5000, CF5- 5000 NPV, I = 8 scroll down, cpt

If you still donate the $100,000 from the previous problem (investment made today), but ask the college to delay the scholarship payment so that the first scholarship payment is made 10 years from today, then how large will the annual payment be? Recall that the interest rate is 5%. Round to the nearest whole dollar.

$7757 PV = -100000 N = 9, because it gets disbursed the 10th year I = 5 FV = ? FV = 155,132.82 155,132.82*0.05 = 7757

Suppose that three years ago you borrowed $25,000 to purchase a car. The terms of the loan required monthly payments over five years at an interest rate of 4.5%. Now, you want to pay the loan off in full. How much do you still owe? Round to the nearest whole dollar.

$10678 Find Pmt 12 p/y PV = 25000 N = 60 I = 4.5 Pmt = ? Pmt = 466.08 Find PV 12 p/y N = 24 I = 4.5 Pmt = -466.08 PV = ? PV = 10678 On old calculator, Shift AMORT 3x Balance = 10678

An annuity due is set up that will pay $1500 per year for ten years. What is the present value (PV) of this annuity given that the discount rate is 8%? Round to the nearest whole dollar.

$10870 Bgn mode Pmt = 1500 N = 10 I = 8 PV = ? PV = 10870

You are borrowing money to buy a car. If you can make payments of $360 per month starting one month from now at an interest rate of 6.2%, how much will you be able to borrow for the car today if you finance the amount over 4 years?

$15269.23 12 p/y Pmt = 360 I = 6.2 N = 48 PV = ? PV = 15269.23

You are saving money to buy a car. If you save $310 per month starting one month from now at an interest rate of 3.5%, how much will you be able to spend on the car after saving for 4 years? Round to the nearest whole dollar.

$15947 switch to 12 p/y Pmt = 310 I = 3.5 N = 48, because 12*4=48 FV = ? FV = 15947

Suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their child's college education. They decide to make deposits into an educational savings account on each of their daughter's birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 9%. The parents deposit $2400 on their daughter's first birthday and plan to increase the size of their deposits by 7% each year. Assuming that the parents have already made the deposit for their daughter's 18th birthday, then the amount available for the daughter's college expenses on her 18th birthday is closest to ________.

$160462.58 Find PV PV = C/r-g * (1 - (1+g/1+r)^n) 2400/.09-.07 = 120000 120000 * (1 - (1.07/1.09)^18) = 34017.0618 Find FV PV = 34017.06 N = 18 I = 9 FV = ? FV = 160462.58

Assume you can earn 9% per year on your investments. If you invest $100,000 for retirement at age 30, how much will you have 35 years later for retirement?

$2,041,396.79 PV = 100000 I = 9 N = 35 FV = ? FV = 2041396.79

You want to endow a scholarship that will pay $10,000 per year forever, starting one year from now. If the school's endowment discount rate is 4%, what amount must you donate to endow the scholarship?

$250,000 PV perpetuity = C/r 10000/.04 = 250000

What is the present value of the following set of cash flows, discounted at 15% per year? Year 1- $100 Year 2- -$100 Year 3- $200 Year 4- -$200

$28.50 Calculator CF Cf1- 100 ENTER, scroll down Cf2- -100 ENTER, scroll down Cf3- 200 ENTER, scroll down Cf4- -200 ENTER NPV, 15 = I scroll down, click cpt

Suppose you receive $100 at the end of each year for the next three years. What is the future value in three years at 8% interest?

$324.64 Find NPV, then use at PV for tvm CF, CF1-100, CF2-100, CF3-100 I = 8 NPV = 257.71 PV = 257.71 I = 8 N = 3 FV = ? FV = 324.64

Suppose that five years ago, you borrowed $260,000 to purchase your first home. Terms of the loan required monthly payments over 30 years at an interest rate of 6%. Since then, interest rates have decreased to 3.5%. As such, you want to refinance this loan. If you refinance this loan at the current rate for the remaining period (25 years), how much will you save per month in your monthly payment? Round to the nearest whole dollar.

$348 Find initial pmt 12 p/y PV = 260000 I = 6 N = 360, because 12*30=360 Pmt = ? Pmt = 1558.83 Balance after 60 pmts 12 p/y Pmt = 1558.83 N = 300, balance left after 60 pmts I = 6 PV = ? PV= 241,941 Net Pmt at 3.5% 12 p/y PV = 241,941.12 I = 3.5 N = 300 Pmt = ? Pmt = 1211.21 Savings =old pmt - new pmt 1558.83 - 1211.21 = 348

If you were to make an investment today of $6,000 in return for a payment to you of $1500 in one year's time, $3000 in two years' time, and $3000 in three years' time, what the net present value of this business opportunity if the interest rate is 7% per year?

$471.08 CF0- -6000 CF1- 1500 CF2- 3000 CF3- 3000 NPV, I = 7 NPV = 471.08

You have $100,000 to donate to your college. You want to endow a perpetual scholarship that makes its first payment in 1 year. If the college's discount rate is 5%, how large will the annual scholarship payment be?

$5000 PV perpetuity = C/r 100,000 = C/.05 C = $5000

A perpetuity will pay $900 per year, starting five years after the perpetuity is purchased. What is the present value (PV) of this perpetuity on the date that it is purchased, given that the interest rate is 11%? Round to the nearest whole dollar.

$5390 C/r = pv perpetuity 900/.11 = 8181.82 FV = 8181.82 I = 11 N = 4 PV = ? PV = 5389.62

You have just received a windfall from an investment you made in a friend's business. She will be paying you $10,000 at the end of this year, $20,000 at the end of next year, and $30,000 at the end of the year after that (three years from today). The interest rate is 3.5% per year. What is the present value of your windfall? Round to the nearest whole dollar.

$55390 Calculator CF CF1- 10000 CF2- 20000 CF3- 30000 click NPV, I = 3.5 scroll down, cpt

Assume that you are 30 years old today, and that you are planning on retirement at age 65. You expect your salary to be $42,000 one year from now and you also expect your salary to increase at a rate of 5% per year as long as you work. To save for your retirement, you plan on making annual contributions to a retirement account. Your first contribution will be made on your 31st birthday and will be 8% of this year's salary. Likewise, you expect to deposit 8% of your salary each year until you reach age 65. Assume that the rate of interest is 9%. The present value (PV) (at age 30) of your retirement savings is closest to ________.

$61302.54 PV = C/r-g * (1 - (1+g/1+r)^n) use 3360 as C, because 8% of 42000 use 35 as N because you are 30 and will retire at 65 PV = 3360/.09-.05 * (1 - (1.05/1.09)^35) PV = $61,302.54

You have just received a windfall from an investment you made in a friend's business. She will be paying you $10,000 at the end of this year, $20,000 at the end of next year, and $30,000 at the end of the year after that (three years from today). The interest rate is 3.5% per year. What is the future value of your windfall in three years (on the date of the last payment)? Round to the nearest whole dollar.

$61412 Find NPV, use at pv for tvm PV = $55390 I = 3.5 N = 3 FV = ? FV = 61412

Assume you can earn 9% per year on your investments. If you wait until age 40 to invest the $100,000, how much will you have 25 years later for retirement?

$862,308.07 PV = 100000 I = 9 N = 25 FV = ? FV = 862,308.07

Juan wants to fund a growing perpetuity that will pay $10,000 per year to his beloved Alma Mater, starting next year. He wants the annual amount paid to the museum to grow by 3% per year. Given that the interest rate is 8%, how much does she need to fund this perpetuity?

$200000 PV = C/r-g =10000/0.08-.03 =200000

You plan to deposit $700 in a bank account now and $100 at the end of the year. If the account earns 5% interest per​ year, what will be the balance in the account right after you make the second​ deposit?

$835 PV = 700 I = 5 N = 1 FV = ? FV = $735 $735 + $100 = $835

Brittany has $12,000 in her savings account and can save an additional $3600 per year. If interest rates are 12%, how many years will it take her savings to grow to $47,000?

5.3 years PV = -12000 Pmt = -3600 I = 12 FV = 47000 N = ? N = 5.3

A businessman wants to buy a truck. The dealer offers to sell the truck for either $120,000 now, or six yearly payments of $25,000. Which of the following is closest to the interest rate being offered by the dealer?

6.8% PV = -120000 N = 6 Pmt = 25000 I = ? I = 6.8%

You owe $5,000 on your credit card and you can pay the following monthly payments: Month 1- 500 Month 2- 550 Month 3- 600 Month 4- 650 Month 5- 700 Month 6- 750 Month 7- 800 Month 8- 850 IF the credit card company charges an interest rate of 1.5% per month, is this enough to pay off your credit card, and if so, by how much?

Yes, this cash flow will pay off the credit card with $23.75 remaining Calculator CF CF1 - 500, Enter, scroll down CF2- 550, Enter, scroll down So on until you get to CF8 Click NPV, enter I = 1.5 scroll down, click cpt $5023.75 - $5000 = $23.75