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butalik [34]
3 years ago
7

A 20-year-old student wants to save $5 a day for her retirement. Every day she places $5 in a drawer. At the end of each year, s

he invests the accumulated savings ($1,825) in a brokerage account with an expected annual return of 8%. If she keeps saving in this manner, how much will she have accumulated at age 65? If a 40-year-old investor began saving in this manner, how much would he have at age 65? How much would the 40-year-old investor have to save each year to accumulate the same amount at 65 as the 20-year-old investor?
Business
1 answer:
ollegr [7]3 years ago
7 0

Answer:

Instructions are listed below

Explanation:

Giving the following information:

At the end of each year, she invests the accumulated savings ($1,825) in a brokerage account with an expected annual return of 8%. She will invest for 45 years.

A) We need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

FV= {1825[(1.08^45)-1]}/0.08= $705,372.75

B) n= 25

FV= {1825[(1.08^25)-1]}/0.08= $133,418.34

C) FV= 705,372.75     A=?

We need to isolate A:

A= (FV*i)/{[(1+i)^n]-1}

A=(705,372.75*0.08)/[(1.08^25)-1]

A= $9,648.64

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Cully Furniture buys two products for resale: king beds (K) and queen beds (Q). Each king bed costs $500 and requires 100 cubic
lana66690 [7]

Answer:

1) 500K + 250Q ≤ 80,000

  100K+80Q≤ 30,000

K≥0

Q≥0

P= 400K + 200Q

2) zero king beds and 320 queen beds

or zero queen beds and 160 king beds

3) surplus variable

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values of surplus variable is 14,000 cubic feet if zero queen beds and 160 king beds

value of surplus variable is 4,400 cubic feet if zero king beds and 320 queen beds.

surplus is the extra amount available after all resources have been utilized to theri maximum.

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Explanation:

1) Implicit variables: K≥0 ;   Q ≥ 0

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500K + 250Q ≤ 80,000-------------------------- from investment constraint

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LP:  P= 400K + 200Q

2) See the attachment for profit maximization graph

3) From graph in the attachment, it can be inferred that storage space is the surplus variable since graph of that equation lies completely outside of optimal area.

Also,

if K=160 and Q=0, the inequality of investment gives

500(160) + 250(0)= 80,000

if K=0 and Q=320, the inequality of investment gives

500(0)+ 250(320) =80,000

if K=0 and Q = 320, the inequality of space gives

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surplus= 30,000- 25,600= 4,400

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surplus= 30000-16000= 14000

4) K=0 and Q=300

investment inequality gives

500(0) + 250(300) ≤ 80,000

75,000≤ 80,000

space inequality gives

100(0) + 80(300) ≤ 30,000

24,000≤ 30,000

Both space and investment are in surplus

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3 years ago
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