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

Instructions are listed below.

Explanation:

Giving the following information:

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