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Bill starts a retirement fund at age 21 and plans on depositing equal annual amo

ID: 2637466 • Letter: B

Question

Bill starts a retirement fund at age 21 and plans on depositing equal annual amounts on each birthday, starting at age 21, and ending at age 60. He wants to have $2 million at age 60. John starts his fund on his 30th birthday. He wants to deposit equal annual amounts on each birthday starting on his 30th birthday and ending on his 60th birthdayJohn wants to have $2 million at age 60. If the investment funds earn 10% per year, calculate the amounts the Bill and John respectively will have to save each year (rounded to the nearest dollar) to meet their goals. Comment on the difference.

Explanation / Answer

Formula to calculate the yearly deposit when the future value of the deposit, number of instalments to be made and interest rate is known is as below:

Deposit amount = Future value* (i/(1+i)^n-1)

In the case of bill future value targeted is $2,000,000

Interest rate=10% hence i=.1

N = 40 as he is willing to deposit every year for 40 years.

Substituting the values in the formula

Yearly payment= $2,000,000*(.1/(1+.1)^40-1)

Yearly payment = $4,519

In case of John targeted amount is $2,000,000

No of years he wants to deposit is 31 years hence n=31

Interest amount =10% hence i=.1

Applying the values into formula:

Annual payment = 2,000,000*(.1/(1+.1)^31-1)

Annual payment=$10,993.

Bill had to deposit less amount when compated to john because he started saving much earlier than John