BA 323 CH:5 time value of money hw problems

If you deposit money today in an account that pays 6% annual interest, how long will it take to double your money? Round your answer to two decimal places.

***RULE OF 72= DOUBLE YOUR MONEY i*m=72 6*m=72 m=11.89 Solution N = ?6%PV = 1FVN = 2 $2 = $1 (1.06)N With a financial calculator enter the following: I/YR = 6, PV = -1, PMT = 0, and FV = 2. Solve for N = 11.90 years.

Your parents will retire in 15 years. They currently have $320,000 saved, and they think they will need $1,850,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places.

12.41%

What is the present value of a security that will pay $40,000 in 20 years if securities of equal risk pay 9% annually? Round your answer to the nearest cent.

7137.24

If you deposit $6,000 in a bank account that pays 4% interest annually, how much will be in your account after 5 years? Round your answer to the nearest cent.

7299.92

One year from today you must make a payment of $5,000. To prepare for this payment, you plan to make two equal quarterly deposits (at the end of Quarters 1 and 2) in a bank that pays 8% nominal interest compounded quarterly. How large must each of the two payments be? Round your answer to the nearest cent

Discount the $5,000 back 2 quarters to find the required value of the 2-period annuity at the end of Quarter 2, so that its FV at the end of the 4th quarter is $5,000.Using a financial calculator enter N = 2, I/YR = 2, PMT = 0, FV = 5,000, and solve for PV = $4,805.84. Step 2:Now you can determine the required payment of the 2-period annuity with a FV of $4,805.84.Using a financial calculator, enter N = 2, I/YR = 2, PV = 0, FV = 4,805.84, and solve for PMT = $2,379.13.

You have $39,346.68 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $260,000. You expect to earn 13% annually on the account. How many years will it take to reach your goal? Round your answer to two decimal places at the end of the calculations.

PV = -39,346.68; PMT = -5,000; FV = 260,000; N = ?; Solve for N = 11. It will take 11 years to accumulate $260,000.

You plan to make five deposits of $1,000 each, one every 6 months, with the first payment being made in 6 months. You will then make no more deposits. If the bank pays 8% nominal interest, compounded semiannually, how much will be in your account after 3 years? Round your answer to the nearest cent.

Since the first payment is made 6 months from today, we have a 5-period ordinary annuity. The applicable interest rate is 8%/2 = 4%. First, we find the FVA of the ordinary annuity in period 5 by entering the following data in the financial calculator: N = 5, I/YR = 8/2 = 4, PV = 0, and PMT = -1,000. We find FVA5 = $5,416.32. Now, we must compound this amount for 1 semiannual period at 4%. $5,416.32(1.04) = $5,632.97.

You plan to make five deposits of $1,000 each, one every 6 months, with the first payment being made in 6 months. You will then make no more deposits. If the bank pays 3% nominal interest, compounded semiannually, how much will be in your account after 3 years? Round your answer to the nearest cent.

Since the first payment is made 6 months from today, we have a 5-period ordinary annuity. The applicable interest rate is 3%/2 = 1.5%. First, we find the FVA of the ordinary annuity in period 5 by entering the following data in the financial calculator: N = 5, I/YR = 3/2 = 1.5, PV = 0, and PMT = -1,000. We find FVA5 = $5,152.27. Now, we must compound this amount for 1 semiannual period at 1.5%. $5,152.27(1.015) = $5,229.55.

one year from today you must make a payment of $8,000. To prepare for this payment, you plan to make two equal quarterly deposits (at the end of Quarters 1 and 2) in a bank that pays 3% nominal interest compounded quarterly. How large must each of the two payments be? Round your answer to the nearest cent.

Step 1:Discount the $8,000 back 2 quarters to find the required value of the 2-period annuity at the end of Quarter 2, so that its FV at the end of the 4th quarter is $8,000.Using a financial calculator enter N = 2, I/YR = 0.75, PMT = 0, FV = 8,000, and solve for PV = $7,881.34 .Step 2:Now you can determine the required payment of the 2-period annuity with a FV of $7,881.34.Using a financial calculator, enter N = 2, I/YR = 0.75, PV = 0, FV = 7,881.34, and solve for PMT = $3,925.95.

PV of a cash flow streams. A rookie quarterback is negotiating his first NFL contract. His opportunity cost is 10 percent. He has been offered three possible 4-year contracts. Payments are guaranteed, and they would be made at the end of each year. Terms of each contract are listed below: As his advisor, which would you recommend that he accept? 1 2 3 4 Contract1 $3,000,000 $3,000,000 $3,000,000 $3,000,000 Contract2 $2,000,000 $3,000,000 $4,000,000 $5,000,000 Contract3 $7,000,000 $1,000,000 $1,000,000 $1,000,000

To solve this problem, you present value each of the future cashflows to today. The payment made after 1 year is worth X / (1+10%)^1 today. The payment made after 2 years is worth X / (1+10%)^2 today. Etc.So, the value of contract 1 is:= $3MM/(1.1) + $3MM/(1.1)^2 + $3MM/(1.1)^3 + $3MM/(1.1)^4 =$9,509,596.34 Contract 2 = $10,717,847.14 Contract 3 = $8,624,410.90. So Contract 2 is the most valuable.

You have saved $5,000 for a down payment on a new car. The largest monthly payment you can afford is $300. The loan will have a 12% APR based on end-of-month payments. What is the most expensive car you can afford if you finance it for 48 months? Do not round intermediate calculations. Round your answer to the nearest cent.$ What is the most expensive car you can afford if you finance it for 60 months? Do not round intermediate calculations. Round your answer to the nearest cent.

a. 16392.19 Financed 48: N=48 . y/IR=(12%/12)=1 PMT=-300 FV=0 then pv= ______ + 5000 saved =16392.19 b. 18486.51 N=60 y/i= 1 PMT=-300 FV=0 so pv= ________ +3000 saved = 18486.51

You have saved $3,000 for a down payment on a new car. The largest monthly payment you can afford is $500. The loan will have a 12% APR based on end-of-month payments. What is the most expensive car you can afford if you finance it for 48 months? Do not round intermediate calculations. Round your answer to the nearest cent What is the most expensive car you can afford if you finance it for 60 months? Do not round intermediate calculations. Round your answer to the nearest cent.

a. 21,968.98 Financed 48: N=48 . y/IR=(12%/12)=1 PMT=-500 FV=0 then pv= 18968.98 + 3000 saved =21,968.98 b. 25,477.52 N=60 y/i= 1 PMT=-500 FV=0 so pv= 22477.52 +3000 saved =25,477.52

your client is 40 years old, and she wants to begin saving for retirement, with the first payment to come one year from now. She can save $5,000 per year, and you advise her to invest it in the tock market, which you expect to provide an average return of 9% in the future. a. if she follows your advice, how much money would she have at 65? b. at 70? c. if she expects to live for 20 years in retirement if she retires at 65 and for 15 years at 70, and her investments continue to earn the same rate, d. how much could she withdraw at the end of each year after retirement at ach retirement age?

a. PMT= -5000 N=25 I=9% PV=0 FV=?FV= $423,504.48 b. PMT= -5000 N=30 I=9% PV=0 FV=?FV= $681,537.69 c. (1) PV= -$423,504.48 *N=20 I=9% FV=0 PMT= ?PMT= $46,393.42(2) PV= -$681,537.69 *N=15 I=9% FV=0 PMT= ?PMT= $84,550.80

Simon recently received a credit card with an 14% nominal interest rate. With the card, he purchased an Apple iPhone 5 for $370. The minimum payment on the card is only $20 per month. a. If Simon makes the minimum monthly payment and makes no other charges, how many months will it be before he pays off the card? Do not round intermediate calculations. Round your answer to the nearest month. month(s) b. If Simon makes monthly payments of $60, how many months will it be before he pays off the debt? Do not round intermediate calculations. Round your answer to the nearest month. month(s) c. How much more in total payments will Simon make under the $20-a-month plan than under the $60-a-month plan. Do not round intermediate calculations. Round your answer to the nearest cent.

a. Using the information given in the problem, you can solve for the length of time required to pay off the card. I/YR = 1.166667 (14%/12); PV = 370; PMT = -20; FV = 0; and then solve for N = 20.961 ≈ 21 months b. If Simon makes monthly payments of $60, we can solve for the length of time required before the account is paid in full. I/YR = 1.166667; PV = 370; PMT = -60; FV = 0; and then solve for N = 6.437 ≈ 6 months. With $60 monthly payments, Simon will only need 6 months to pay off the account. c. Total payments @ $20/month:20.961 x $20 =$419.22-Total payments @ $60/month:6.437 x $60 =-386.22 . Extra interest =$33.00

An investment will pay $50 at the end of each of the next 3 years, $200 at the end of Year 4, $300 at the end of Year 5, and $600 at the end of Year 6. If other investments of equal risk earn 7% annually, what is its present value? Round your answer to the nearest cent. $ If other investments of equal risk earn 7% annually, what is its future value? Round your answer to the nearest cent. $

pv=897.50 Present Value = $ 50 * 1/(1.07) ^ 1 + $ 150 * 1/(1.07) ^ 2 +$ 50 * 1/(1.07) ^3 + $ 200 * 1/(1.07) ^4 + $ 300 * 1/(1.07) ^5 +$ 600 * 1/(1.07) ^6 fv=1346.90 To solve for the FV of the cash flow stream with a calculator that doesn't have the NFV key, do the following: Enter N = 6, I/YR = 7, PV = -897.50, and PMT = 0. Solve for FV = $1,346.91.