PRACTICE AND CLASS ch. 5 (Time value of money)

C 1. Hanni decides to buy a 2015 Harley today that costs $25,600. She has enough for a $5,000 down payment. The Harley dealer offers an interest rate at 6.5% annual, compounded monthly on a 5-year loan. What is the monthly payment Hanni must pay to have her hog?

SOLUTION: PMT -$403.06 PV 20600 =25600-5000 I 0.541666667 =6.5/12 N 60 =5*12

P 1. Bekki wants to travel to Thailand in 15 years. Today a plane ticket cost $750 and the average annual inflation rate is 3.22%. How much should Bekki expect to pay for her plane ticket in 15 years?

SOLUTION: $1,206.48

P 10. Helga just told her parents, Hannah & Eli, all about the dream man she met at BYU, Fredrick. Helga and Fredrick both plan on going on missions and perhaps a study abroad. Hannah & Eli figure they have 3 years to save for Helga's wedding. If they put $300 every month into a savings account that gets 6% compounded monthly, how much money will they have for Helga's wedding in 3 years?

SOLUTION: $11,800.83 PV: 0 PMT: -300 N: 3*12 I: 6/12 FV: 11,800.83

P 5. You think you're the next Taylor Swift but nobody believes in you, so you will have to finance your own album recording yourself. It costs $5,000 to record an EP but you only have $1,000 saved up. How much do you need to set aside every month if you get 9% compounded monthly in your savings account and you want to record in 12 months?

SOLUTION: $312.31 every month PV: 1,000 PMT: 312.31 FV: -5,000 RATE: 9/12 PERIODS: 12

P 8. Kenzie loves puppies and wants to donate $2,500 every year forever to Puppies 4 People. If the discount rate is 7%, how much does Kenzie need to set aside today?

SOLUTION: $35,714.29 PV perpetuity = PMT/I PMT 2,500 I .07

P 3. Hannah and Eli just had their first child, a little girl named Helga. They want to be fiscally responsible and start saving for Helga's college education. They want $20,000 saved up in 18 years. If they use their saving account, which earns 8% annually, how much do they need to put aside today for Helga's college fund?

SOLUTION: $5,004.98 PV: 5004.98 PMT: 0 FV: 20,000 RATE: 8% PERIODS: 18

P 4. Congrats! You just landed your dream job as an accountant for Vivint Smart Home Arena. You're 24 and planning to retire in 42 years. If your retirement account pays an annual rate of 5% compounded monthly and you deposit $300 every month, how much money will you have when you retire?

SOLUTION: $513,404.60 PV: 0 PMT: 300 FV: 513404.6 RATE: 5/12 PERIODS: 42*12

P 6. You bought a car today for $30,000. (It must have used up all of your summer sales funds!) You financed the car with a 5 year loan at 3.6%. If you start making payments at the end of each month starting next month, how expensive are your monthly payments?

SOLUTION: $547.10 PV: -30,000 PMT: 547.10 FV: 0 RATE: 3.6/12 N: 5 * 12 = 60

P 2. This past summer Samantha and Kirsten ran a lemonade stand. Because they are cute six year-old twins and great salesmen, they were able to make $5,000 during the summer. They want to leave their money in a savings account for 10 years until they can buy a car. If they earn 7% in their savings account, how much will they have when they are 16 years old?

SOLUTION: $9,835.76

P 9. Fredrick is a freshman at BYU and is planning to meet the girl of his dreams here. He wants to buy her the ring of her dreams and figures he has 4 years to save for it in a savings account that gets 12% compounded monthly. He currently has $200 in his savings and plans to add $50 every month for the next 4 years. How much money will he have for a ring at the end of those 4 years?

SOLUTION: 3383.58 PV -200 PMT -50 I 12/12 N 4 *12 FV 3383.58

P 7. All Jared wants in life is to be a millionaire. If he put $10,000 into a savings account that gets 8% compounded semi-annually, how long will it take him to become a millionaire?

SOLUTION: 58.7 years. Don't forget to change the number from semi-annual PV -10,000 FV 1,000,000 PMT 0 I 8/2 N 117.4 /2 = 58.7

C 4. Big Heber decides he wants to buy a super computer when he gets back from his mission. He has $200 to invest today and he plans to invest $100 a month beginning at the end of this month for the next five years. He feels he can earn a 2% annual return, compounded monthly. How expensive of a computer will he be able to buy?

SOLUTION: FV $6,525.75 PV -200 PMT -100 N 60 =5*12 I 0.166666667 =2/12

C 6. The Gunnels want to start a college account for Baby Hunter. They figure he will start college in 19 years after his mission. They have $1,000 to put away right now and they plan to invest $50 per week, in a weekly compounded investment that carries a 4% annual interest rate. How much will Baby Hunter's college account be in 19 years?

SOLUTION: FV $76,085.01 N 988 =19*52 PV -1000 PMT -50 I 0.076923077 =4/52

C 3. Lulu decides to invest in a bond. The future value (face value) of the bond is $1,000. She can buy the bond today for $970. It has a three year maturity and pays semi-annual coupons (payments). The bond pays $20 every six months as the coupon payment. What is the interest rate (yield to maturity) on the bond: Six month? One year?

SOLUTION: I 2.55% semi-annual 5.09 annual FV 1000 PV -970 N 6 PMT 20

C 5. In 1947, right after WWII ended, Pap Pap decided to invest in a real estate property. At the time, he purchased it for $15,000. In 1997, when he passed away, the property was worth $1,000,000. What was the return earned on the property assuming annual compounding?

SOLUTION: I 8.76% N 50 PV -15000 FV 1,000,000

C 2. Bunny decides to buy a fireplace, but thinks she should save the money. She hopes to have $3,500 in 2 years. She feels she can invest at 1% annual, compounded monthly. She has $200 to put down on the fireplace now and will pay the rest in monthly payments. How big must her monthly payments be?

SOLUTION: PMT -$136.02 FV 3500 N 24 =2*12 PV -200 I 0.083333333 =1/12

C 8. For the problem in 7, what is the present value today (19 years from start of college) of the total tuition costs if the discount (interest) rate is 4% compounded monthly? (assuming end mode)

SOLUTION: PV $9,093.29 FV -19419.41636 From 7 I 0.333333333 =4/12 N 228 =19*12

C 7. Tuition must be paid at the beginning of the year beginning in 19 years for Baby Hunter. Assuming that tuition costs $5,000 at the beginning of the year starting on his 19th birthday, and continues for a total of four years, if the opportunity cost (interest rate) is 2% compounded annually how much is the present value of the total tuition costs when Hunter starts college?

SOLUTION: PV -$19,419.42 Which is 19 years in the future PMT 5,000 BEGIN MODE N 4 I 2