Sara's Strategy: On each of her birthdays, beginning on her 20th and ending on her 30th, Sara deposits $1000 in an investment account (a total of 11 deposits). After her 30th birthday deposit, she leaves the total amount in her account but does not add anything to it. Joe's Strategy: On each of his birthdays, beginning on his 30th, Joe continues to deposit $1000 in an investment account. The table represents the amount of money (rounded to the nearest dollar) in Sara's and Joe's respective accounts on their birthdays after any deposits are made (if any are made) up until age 62. Also, the table of values was created under the assumption that both Sara and Joe are investing in the same type of account that earns 8% interest compounded continuously. a. When Sara is 40 years old, how much will she have in her account? b. When Joe is 40 years old, how much will he have in his account? c. Find the percentage increase in Sara's account between age 50 and 54.

Sara's Strategy: On each of her birthdays, beginning on her 20th and ending on her 30th, Sara deposits $1000 in an investment account (a total of 11 deposits). After her 30th birthday deposit, she leaves the total amount in her account but does not add anything to it. Joe's Strategy: On each of his birthdays, beginning on his 30th, Joe continues to deposit $1000 in an investment account. The table represents the amount of money (rounded to the nearest dollar) in Sara's and Joe's respective accounts on their birthdays after any deposits are made (if any are made) up until age 62. Also, the table of values was created under the assumption that both Sara and Joe are investing in the same type of account that earns 8% interest compounded continuously. a. When Sara is 40 years old, how much will she have in her account? b. When Joe is 40 years old, how much will he have in his account? c. Find the percentage increase in Sara's account between age 50 and 54.

Name: Sara and Joe are two students who are the same age, share the same bi
Uploaded: 2024-03-20T07:07:26.000Z
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Description: Sara and Joe are two students who are the same age, share the same birthday, and areplanning for their eventual retirement. The task for this problem is to compare each oftheir retirement investment strategies by analyzing the information provided a

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Sara and Joe are two students who are the same age, share the same birthday, and are
planning for their eventual retirement. The task for this problem is to compare each of
their retirement investment strategies by analyzing the information provided and then
answering the questions that follow.
Note: No formulas are necessary to answer the questions asked in this problem. Please
analyze and use only the information provided in answering the parts to this question.
Sara's Strategy: On each of her birthdays, beginning on her 20th and ending on her 30th,
Sara deposits $1000 in an investment account (a total of 11 deposits). After her 30th
birthday deposit, she leaves the total amount in her account but does not add anything to
it.
Joe's Strategy: On each of his birthdays, beginning on his 30th, Joe continues to deposit
$1000 in an investment account.
The table represents the amount of money (rounded to the nearest dollar) in Sara's and
Joe's respective accounts on their birthdays after any deposits are made (if any are made)
up until age 62. Also, the table of values was created under the assumption that both
Sara and Joe are investing in the same type of account that earns 8% interest compounded
continuously.
a. When Sara is 40 years old, how much will she have in her account?
b. When Joe is 40 years old, how much will he have in his account?
c. Find the percentage increase in Sara's account between age 50 and 54.

Erika's
d. At what age will Joe catch up to Sara?
e. At age 62, how much total out-of-pocket money has Sara deposited in her account? f.
At age 62, how much total out-of-pocket money has Joe deposited in his account?
mate the
Age Value of Sara's Acct Value of Joe's Acct
20 $1,000 $0
40 $37,701 $16,940
21 $2,083 $0
41 $40,841 $19,351
Nar
22 $3,257 $0
42 $44,243 $21,963
Din
Any
on t
23 $4,528 $0
43 $47,928 $24,792
and
sent
24 $5,905 $0
44 $51,919 $27,857
type
writt
is yo
instr
your
25 $7,397 $0
45 $56,243 $31,177
26 $9,013 $0
46 $60,928 $34,774
27 $10,764 $0
47 $66,002 $38,670
The f
Corre
on the
28 $12,660 $0
48 $71,499 $42,891
29 $14,715 $0
49 $77,454 $47,463
SUN
30 $16,940 $1,000
50 $83,905 $52,416
Outc
31 $18,351 $2,083
51 $90,894 $57,781
SUN
32 $19,880 $3,257
52 $98,464 $63,594
(Inte
33 $21,535 $4,528
53 $106,665 $69,890
SUN
34 $23,329 $5,905
54 $115,548 $76,711
35 $25,272 $7,397
55 $125,172 $84,100
36 $27,377 $9,013
56 $135,597 $92,105
37 $29,657 $10,764
t57 $146,891 $100,776
38 $32,127 $12,660
58 $159,125 $110,169
39 $34,803 $14,715
59 $172,378 $120,345
60 $186,735 $131,368
61 $202,287 $143,309
62 $219,135 $156,245

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