FIN 323 Chapter 5 Homework Practice for Exam

First City Bank pays 8 percent simple interest on its savings account balances, whereas Second City Bank pays 8 percent interest compounded annually. If you made a $55,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 8 years?

The time line for the cash flows is: 0 8 Picture $55,000 FV The simple interest per year is: $55,000 × .08 = $4,400 So after 8 years you will have: $4,400 × 8 = $35,200 in interest. The total balance will be $55,000 + 35,200 = $90,200 With compound interest we use the future value formula: FV = PV(1 + r)t FV = $55,000(1.08)8 = $101,801.16 The difference is: $101,801.16 - 90,200 = $11,601.16 Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. Enter 8 8% ±$55,000 N =8 I/Y = .8 PV = 55000 PMT = FV = 101801.16 Solve for $101,801.16 $101,801.16 − 90,200 = $11,601.16

Assume the total cost of a college education will be $250,000 when your child enters college in 17 years. You presently have $69,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child's college education?

To answer this question we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)^t Solving for r, we get: r = (FV / PV)^(1/t) - 1 r = ($250,000 / $69,000)^(1/17) - 1 r = .0787, or 7.87% Calculator Solution: Enter N=17 PV=69000 FV=250000 Solve for I/Y: 7.87%

In 1895, the first Putting Green Championship was held. The winner's prize money was $190. In 2014, the winner's check was $1,490,000. What was the percentage increase per year in the winner's check over this period? If the winner's prize increases at the same rate, what will it be in 2044?

To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)^t Solving for r, we get: r = (FV / PV)^(1/t) - 1 r = ($1,490,000 / $190)^(1/119) - 1 r = .0783, or 7.83% To find the FV of the first prize in 2044, we use: FV = PV(1 + r)t FV = $1,490,000(1.0783)30 FV = $14,288,150.51 Calculator Solution: Enter N=119 PV=190 FV=1490000 Solve for I/Y: 7.83 Enter N=30 I/Y=7.83 PV=1490000 Solve for FV: 14288150.51

Assume that in January 2013, the average house price in a particular area was $273,400. In January 2002, the average price was $190,300. What was the annual increase in selling price?

To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)^t Solving for r, we get: r = (FV / PV)^(1/t) - 1 r = ($273,400 / $190,300)^(1/11) - 1 r = .0335, or 3.35% Calculator Solution: Enter N=11 PV=190300 FV=273400 Solve for I/Y: 3.35%

You're trying to save to buy a new $196,000 Ferrari. You have $46,000 today that can be invested at your bank. The bank pays 5.4 percent annual interest on its accounts. How long will it be before you have enough to buy the car?

To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)^t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) t = ln($196,000 / $46,000) / ln(1.054) t = 27.56 years Calculator Solution: Enter I/Y=5.4% PV=46000 FV=196000 Solve for N: 27.56

For each of the following, compute the future value: Present Value Years Interest Rate Future Value $ 1,950 10 14 % $ 8,152 8 8 70,355 15 13 177,796 6 5

To find the FV of a lump sum, we use: FV = PV(1 + r)t 0 10 Picture $1,950 FV FV = $1,950(1.14)10 = $7,229.08 0 8 Picture $8,152 FV FV = $8,152(1.08)8 = $15,088.78 0 15 Picture $70,355 FV FV = $70,355(1.13)15 = $440,019.19 0 6 Picture $177,796 FV FV = $177,796(1.05)6 = $238,263.64 Calculator Solution: Enter: 10=N 14%=I/Y 1950=PV PMT= Solve for: 7229.08 = FV Enter: 8=N 8%=I/Y 8152=PV PMT= Solve for: 15088.78 = FV Enter: 15=N 13%=I/Y 70355=PV PMT= Solve for: 440019.19 = FV Enter: 6=N 5%=I/Y 177796=PV PMT= Solve for: 238263.64 = FV

You have just received notification that you have won the $2 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you're around to collect), 67 years from now. What is the present value of your windfall if the appropriate discount rate is 9 percent?

To find the PV of a lump sum, we use: PV = FV / (1 + r)^t PV = $2,000,000 / (1.09)^67 PV = $6,215.19 Calculator Solution: Enter N=67 I/Y=9% FV=2000000 Solve for PV: 6215.19

For each of the following, compute the present value: Years=12, IR=6%, FV=$15,051 Years=3, IR=12%, FV=$47,557 Years=28, IR=13%, FV=$882,073 Years=30, IR=10%, FV=$546,164

To find the PV of a lump sum, we use: PV=FV / (1+r)^t PV=15051 / (1.06)^12 = 7479.89 PV = $47,557 / (1.12)^3 = $33,850.13 PV = $882,073 / (1.13)^28 = $28,794.41 PV = $546,164 / (1.10)^30 = $31,299.87 Calculator Solution: Enter: 12=N, 6%=I/Y, FV=15051 Solve for: PV = 7479.89 continue

Solve for the unknown interest rate in each of the following: PV=190, Yrs=4, FV=231 PV=310, Yrs=18, FV=854 PV=34000, Yrs=19, FV=148042 PV=33261, Yrs=25, FV=412862

We can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)^t Solving for r, we get: r = (FV / PV)^(1 / t) - 1 FV = $231 = $190(1 + r)^4 r = ($231 / $190)^(1/4) - 1 r = .0501, or 5.01% continue Calculator Solution: Enter N=4 PV=190 FV=231 Solve for I/Y: 5.01%

Solve for the unknown number of years in each of the following: PV=630, IR=8%, FV=1496 PV=880, IR=12%, FV=2496 PV=19100, IR=18%, FV=392101 PV=22200, IR=14%, FV=403794

We can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)^t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) FV = $1,496 = $630(1.08)^t t = ln($1,496 / $630) / ln(1.08) t = 11.24 years continue Calculator Solution: Enter I/Y=8% PV=630 FV=1496 Solve for N = 11.24 continue