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Question 14 Bill and Cathy will be retiring in fifteen years and would like to buy...

Question 14

Bill and Cathy will be retiring in fifteen years and would like to buy an Italian villa. The villa costs $500,000 today, and housing prices in Italy are expected to increase by 5.5% per year. Bill and Cathy wants to deposit one lump sum amount today. If their account earns 10% per year, what is the amount of this deposit?

$307,839

$372,623

$286,858

$267,219

Question 15

Susan saved $5000 per year in her retirement account for 10 years (during age 25-35) and then quit saving. However, she did not make any withdrawal until she turned 65 (i.e., 30 years after she stopped saving). Her twin sister, Jane did not save anything during the 1st 10 years (during age 25-30) but saved $5,000 per year for 30 years (during age 35-65). What will be the difference in their retirement account balance at age 65, if their investments earned an average return of 7.5% during the entire period?

$162,450

$102,289

$53,568

$236,265

Solutions

Expert Solution

14.

Present Value of the villa = PV = $500000

Inflation rate = i = 5.5%

Number of years = n = 15

Future Value of Villa = FV = PV(1+i)n = 500000(1+0.055)15 = $1116238.25

Let the lumpsum deposited today be P

Interest rate earned = r = 10%

Future Value required = FV = $1116238.25

=> P(1+r)n = 1116238.25

=> P(1+0.10)15 = 1116238.25

=> P = 1116238.25/(1+0.10)15 = $267219

15.

Susan

Amount deposited each year = P = $5000

Number of years = n = 10

Interest Rate = r = 7.5%

Value in Account after 10 years X = P(1+r)n-1 +....+ P(1+r)2 + P(1+r) + P = P[(1+r)n -1]/r = 5000[(1+0.075)10 -1]/0.075 = $70735.44

Value of X after 30 years = X(1+r)30 = 70735.44(1+0.075)30 = $619285.61

Jane

Amount saved each year = P = 5000

Number of years = n = 30

Interest rate = r = 7.5%

Amount in account after 30 years = P(1+r)n-1 +....+ P(1+r)2 + P(1+r) + P = P[(1+r)n -1]/r = 5000[(1+0.075)30 -1]/0.075 = $516997.01

Difference in amount = 619285.61 - 516997.01 = $102289


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