Question

In: Finance

Over the past several years, Catherine Lee has been able to save regularly. As a result,...

Over the past several years, Catherine Lee has been able to save regularly. As a result, she has $58,467 in savings and investments today. She wants to establish her own business in four years and feels she will need $100,000 to do so. Use the following table to answer the questions.

  1. If she can earn 3% on her money, how much will her $58,467 in savings/investments be worth in 4 years? Round the answer to the nearest cent. Round FV-factor to three decimal places.
    Calculate your answer based on the FV-factor.

    $  


    Calculate your answer based on the financial calculator.

    $  


    Will Catherine have the $100,000 she needs?
    -Select-Yes/No?

    If not, how much more money will she need? Round the answer to the nearest cent. Round FV-factor to three decimal places.
    Calculate your answer based on the FV-factor.

    $  


    Calculate your answer based on the financial calculator.

    $  

  2. Given your answer to part a, how much will Catherine have to save each year over the next 4 years to accumulate the additional money? Assume that she can earn interest at a rate of 3%. Round the answer to the nearest cent. Round FVA-factor to three decimal places.
    Calculate your answer based on the FVA-factor.

    $  


    Calculate your answer based on the financial calculator.

    $  

  3. If Catherine can afford to save only $4,000 a year, then given your answer to part a, will she have the $100,000 she needs to start her own business in 4 years?
    -Select-Yes/No?

Solutions

Expert Solution

Answer a.

Using FV-factor:

Current Saving = $58,467
Desired Balance after 4 years = $100,000
Interest Rate = 3%

Accumulated Sum = $58,467 * FV of $1 (3%, 4)
Accumulated Sum = $58,467 * 1.126
Accumulated Sum = $65,833.84

She will need $34,166.16 ($100,000 - $65,833.84) more

Using financial calculator:

Current Saving = $58,467
Desired Balance after 4 years = $100,000
Interest Rate = 3%

I = 3%
N = 4
PV = -58467
PMT = 0

FV = 65805.12

Accumulated Sum = $65,805.12

She will need $34,194.88 ($100,000 - $65,805.12) more

Answer b.

Current Saving = $58,467
Desired Balance after 4 years = $100,000
Interest Rate = 3%

Using FVA-factor:

$58,467 * FV of $1 (3%, 4) + Annual Deposit * FVA of $1 (3%, 4) = $100,000
$58,467 * 1.126 + Annual Deposit * 4.184 = $100,000
$65,833.84 + Annual Deposit * 4.184 = $100,000
Annual Deposit * 4.184 = $34,166.16
Annual Deposit = $8,165.91

Using financial calculator:

N = 4
I = 3%
PV = -58467
FV = 100000

PMT = 8173.50

Annual Deposit = $8,173.50

Answer c.

No, If Catherine only saved $4,000 a year, then she will not have $100,000 in 4 years.

jeff jeffy answered 1 year ago
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