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FIN 323 Chapter 5 Homework Practice for Exam

Terms in this set (10)

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
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
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
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%
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
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
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
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