Gilbert needs $600,000 (in today's dollars) when he retires in 20 years to open a lakefront bed and breakfast. He has saved $150,000 (current balance) toward this goal. Gilbert anticipates the annual inflation rate over the 20-year period will be 4%, and that he can earn an after-tax return of 8% on any invested funds. How much does Gilbert need to save at the start of the 1st year if he makes inflation-adjusted deposits at the beginning of each year

Gilbert needs $600,000 (in today's dollars) when he retires in 20 years to open a lakefront bed and breakfast. He has saved $150,000 (current balance) toward this goal. Gilbert anticipates the annual inflation rate over the 20 years will be 4%, and that he can earn an after-tax return of 8% on any invested funds.

First, we calculate the future value of the lump sum:

FV= PV*(1+i)^n

FV= 150,000*1.04^20= 328,668.47

Now, we determine the future value required in annual deposits:

Rest= 600,000 - 328,668.47= 271,331.53

We need to use the following formula to calculate the annual deposits:

A= {(FV*i)/ {[(1+i)^n] - 1]} / (1+i)

A= {(271,331.53*0.04) / [(1.04^20) - 1]} / 1.04

A= $8,761.33