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In: Finance

THE FOLLOWING DATA APPLY TO THE NEXT THREE PROBLEMS Johnny and Ronny have both been given...

THE FOLLOWING DATA APPLY TO THE NEXT THREE PROBLEMS Johnny and Ronny have both been given $50,000 by their grandparents today on their 21st birthdays. They want to save for their future and have aspirations of one day being millionaires. Both boys plan to make annual contributions on their birthday, beginning next year. Johnny and Ronny have each opened investment accounts at Chase and Wells Fargo, respectively, and they expect to earn nominal returns of 8% and 9% respectively. Johnny has already decided to deposit $8,000 each year into his investment account, while Ronny is unsure of the amount he will deposit annually.

How many years will it take Johnny before he reaches his investment goal of $1 million?

If Ronny decides to make the same annual contributions as Tommy, how much sooner (in years) would he reach the investment goal?

Suppose Ronny was interested in reaching the investment goal at the same time as Johnny. What is the minimum monthly contribution he could make to reach $1 million at the same time as Johnny?

Solutions

Expert Solution

Value of saving at age of 21 year = $50,000.

Return on investment for Johnny = 8%

Return on investment for Ronny = 9%.

a.

Annual Investment by Johnny = $8,000

Number of year it will take to become millionaires is calculated in excel and screen shot provided below:

It will take 26 year for Johnny to become millionaire.

b.

If Ronny decides to make the same annual contributions as Johnny then Number of year it will take to become millionaires is calculated in excel and screen shot provided below:

For Ronny it will take 24 year to become millionaire.

c.

for Johnny it will take 26 year

Future value of current saving at 9% = $50,000 × (1 + 9%) ^ 26

= $50,000 × 9.3095

= $465,476.42.

Future value of current saving at 9% is $465,476.42.

Excess amount required through monthly Saving = $1,000,000 - $465,476.42

= $534,523.58.

Excess amount required through monthly Saving is $534,523.58.

Minimum monthly contribution he could make to reach $1 million at the same time as Johnny is calculated in excel and screen shot provided below:

Value of monthly Saving is $436.28.

jeff jeffy answered 2 years ago
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