Transcript Slide 1

Homework, Page 341
Find the amount A accumulated after investing a principal P for t
years at an interest rate of r compounded annually.
1. P  $1500; r  7%; t  6
P  $1500; r  7%; t  6
A  P 1  r   A  1500 1  0.07   2251.0955
t
6
A  $2251.09
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 3- 1
Homework, Page 341
Find the amount A accumulated after investing a principal P for t
years at an interest rate of r compounded n times per year.
5. P  $1500; r  7%; t  5; k  4
P  $1500; r  7%; t  5; k  4
nt
 r
 0.07 
A  P 1    A  1500 1 

4 
 n

4 5
 2122.167
A  $2,122.16
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 3- 2
Homework, Page 341
Find the amount A accumulated after investing a principal P for t
years at an interest rate of r compounded continuously.
9. P  $1, 250; r  5.4%; t  6
P  $1, 250; r  5.4%; t  6
A  Pert  A  1250e0.054 6  1728.3091
A  $1, 728.30
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Slide 3- 3
Homework, Page 341
Find the future value FV accumulated in an annuity after
investing periodic payments R for t years at an annual interest
rate r with payments made and interest credited k times per year.
13. R  $500; r  7%; t  6; n  4
R  $500; r  7%; t  6; n  4
 0.07 
1
nt


1  i   1
4 

FV  R
 FV  500
0.07
i
4
FV  $14, 755.50
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
4 6
1
 14755.508
Slide 3- 4
Homework, Page 341
Find the present value PV of a loan with annual interest rate r and
periodic payments R for a term of t years, with payments made
and interest charged 12 times per year.
17. r  4.7%; R  $815.37; t  5
r  4.7%; R  $815.37; t  5
 0.047 
1  1 
n

1  1  i 
12 

PV  R
 PV  815.37
0.047
i
12
PV  43523.3098  PV  $43,523.31
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
12 5
Slide 3- 5
Homework, Page 341
Find the periodic payment R of a loan with present value PV and
an annual interest rate r for a term of t years, with payments made
and interest charge 12 times per year.
19.
PV  $18,000; r  5.4%; t  6
12 6
 0.054 
1  1 
 nt

1  1  i 
12

PV  R
 18000  R 
0.054
i
12
0.054
12
R  18000
 293.240  R  $293.24
12 6
 0.054 
1  1 

12 

Slide 3- 6
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Homework, Page 341
21. If John invests $2,300 in a savings account with a
9% interest rate compounded quarterly, how long will it
take until John’s account has a balance of $4,150?
nt
4t
 r
 0.09 
A  P 1    4150  2300 1 

4 
 n

 0.09 
4150  2300 1 

4 

4t
6.631 years or 6 yrs., 8 mos.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 3- 7
Homework, Page 341
25. What interest rate, compounded daily, is required
for a $22,000 investment to grow to $36,500 in 5 years?
nt
r 
 r

A  P 1    36500  22000 1 

n
365




365 5
1825
r 

365  220 1 

365


10.127%
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 3- 8
Homework, Page 341
29. Determine how much time is required for an
investment to double in value if interest is earned at the
rate of 5.75%, compounded quarterly.
kt
 r
 0.0575 
A  P  1    2  1 1 

4 
 k

4t
 t  12.141 years
t  12 years, 2 months
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Slide 3- 9
Homework, Page 341
33. Complete the table about continuous compounding.
Principal
$9,500
APR
?
2X Time
4 years
A(15)
?
ln 2
A  Pe  2  1e  ln 2  4r  r 
 17.329%
4
rt
r4
0.17329
0.17329
1

r

e

r

e
 1  APR  18.921%
 
1
A 15   9500e0.17329 15  $127,822.39
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Slide 3- 10
Homework, Page 341
37. Complete the table about annual compounding.
APR
7%
n
1
2X Time
?
A  P 1  r   2  11  0.07   2  1.07t
t
t
ln 2
ln 2  ln1.07  ln 2  t ln1.07  t 
 10.245
ln1.07
t  10.245 years or 10 years 3 months
t
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Slide 3- 11
Homework, Page 341
Find the annual percentage yield (APY) for the investment.
41. $3,000 at 6% compounded quarterly
nt
t
 r
A  P 1    A  P 1  r 
 n
 0.06 
3000 1 

4 

1.015
4
41
 3000 1  r   1  0.015   1  r 
1
4
 1  r  r  1.061364  1  0.061364  6.14%
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 3- 12
Homework, Page 341
45. Which investment is more attractive, 5%
compounded monthly or 5.1% compounded quarterly?
nt
 r
A  P 1  
 n
n
12
 r   0.05 
1    1 
  1.051162
12 
 n 
n
4
 r   0.051 
1    1 
  1.051984
4 
 n 
Investing at 5.1% compounded quarterly is more
attractive.
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Slide 3- 13
Homework, Page 341
49. Jolinda contributes to the Celebrity Retirement
Fund which earns 12.4% annual interest. What should
her monthly payments be if she wants to accumulate
$250,000 in 20 years?
12 20
 0.124 
1
1
n


1  i   1
12 

FV  R
 250000  R
0.124
i
12
R  $239.41 per month
Jolinda should invest $239.41
per month to reach her goal.
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Slide 3- 14
Homework, Page 341
53. Gendo obtains a 30-year $86,000 house loan with
an APR of 8.75% from National City Bank. What is her
monthly payment
12 30
 0.0875 
1  1 
 nt

1  1  i 
12

PV  R
 86000  R 
0.0875
i
12
R  $676.56 per month
Gendo’s mortgage payment
is $676.56 per month.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 3- 15
Homework, Page 341
57. Explain why computing the APY for an
investment does not depend on the actual amount being
invested.
The APY does not depend on the amount invested,
because both sides of the equation used in computing
APY contain P as a factor, so the equation may be
divided by P, eliminating it as a factor.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 3- 16
Homework, Page 341
57. Give a formula for the APY on a $1 investment at
annual rate r, compounded n times per year. How do
you extend the result to a $1,000 investment?
n
n
 r
 r
P 1  APY   P 1    11  APY   11  
 n
 n
n
n
 r
 r
1  APY  1    APY  1    1
 n
 n
The APY formula given above applies to an investment
of $1,000 without modification.
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Slide 3- 17
Homework, Page 341
61. If $100 is invested at 5% annual interest for one
year, there is no limit to the final value of the
investment if it is compounded sufficiently often.
Justify your answer.
False. The most frequently the interest could be
compounded is continuously and the final value of the
investment after one year of continuous compounding is
a finite number.
A  Pert  A  100e0.05 1  105.13
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Slide 3- 18
Homework, Page 341
65. Mary Jo deposits $300 each month into her
retirement account that pays 4.5% APR. Find the value
of her annuity after 20 years.
240
A. $71, 625.00
1  0.045
1
12
FV  300
B. $72,000.00
0.045
12
C. $72, 375.20
 $116, 437.31
D. $73,453.62
E. $116,437.31

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
Slide 3- 19
Homework, Page 341
69. The function


x
1  0.08
1
12
f  x   100
0.08
12
describes the future value of a certain annuity.
a. What is the annual interest rate.
8% per year
b. How many payments per year are there?
12 payments per year
c. What is the amount of each payment?
$100
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 3- 20