Chapter 12 Sequences; Induction; the Binomial Theorem

Section 12.1: Sequences
c. Find the value of the account in 25 years or
100 quarters:
c. Enter the recursive formula in Y= and create
the table:
The value of the account will be $156,116.15.
88. a. Since the fund returns 6% compounded
annually, this is equivalent to a return of
0.5% each month. Defining a recursive
sequence, we have:
a0 = 0, an
= 1.005an
− 1+
45
b. Insert the formulas in your graphing utility
and use the table feature to find when the
value of the account will exceed $4,000:
d. Scroll through the table:
After 58 payments have been made, the
balance is below $140,000. The balance is
about $139,981.
e. Scroll through the table:
In the 74th month (February 2006) the value
of the account will exceed $4,000 with a
value of about $4,017.60.
c. Find the value of the account in 16 years or
192 months:
The value of the account will be
approximately $14,449.11.
89. a. Since the interest rate is 6% per annum
compounded monthly, this is equivalent to a
rate of 0.5% each month. Defining a
recursive sequence, we have:
a0 = 150,000, an
= 1.005an
− 1−
899.33
b. 1.005(150,000) − 899.33 = $149,850.67
The loan will be paid off at the end of 360
months or 30 years.
Total amount paid = (359)($899.33) +
$890.65(1.005) = $323,754.57.
f. The total interest expense is the difference
of the total of the payments and the original
loan: 323,754.57 − 150,000 = $173,754.57
g. (a) Since the interest rate is 6% per annum
compounded monthly, this is equivalent to
a rate of 0.5% each month. Defining a
recursive sequence, we have:
a0 = 150,000, an
= 1.005an
− 1−
999.33
(b) 1.005(150,000) − 999.33 = $149,750.67
1241
© 2009 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.