Your client, Jeff, would like to have $500,000 in today’s dollars 10 years from now for...

Your client, Jeff, would like to have $500,000 in today’s dollars 10 years from now for retirement. You mutually agree that inflation will stay constant at 3% and you could achieve an average annual return of 10%. Jeff would like the investments to increase each year by inflation. How much would his first payment be if he invested at the end of each year? How much would his first payment be if he invested at the beginning of each year?

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Expert Solution

Value of $500,000 in 10 years from now is the future value, compounded every year at the rate of inflation. The value in 10 years will be $671,958.19 as follows:

FV= PV*(1+i)^n

Where PV= present value ($500,000), i= inflation rate (3%) and n= number of years (10)

Therefore, FV= $500,000*(1+3%)^10= $500,000*1.03^10 =$500,000* 1.343916379= $671,958.19

Investments over 10 years will constitute growing annuity.

If the investments are made at the end of each year, it is an ordinary growing annuity and the first payment shall be $37,634.89 as follows:

If the investments are made at the beginning of each year, it is a growing annuity due and the first payment shall be $34,213.54 as follows:

jeff jeffy answered 6 hours ago

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