Assume that Tom and Barb from Question $6$ will need a lump$-$sum retirement fund of $$5$ million; their assets will amount to $$3$ million at the first retirement year, leaving $$2$ million to be saved over the pre$-$retirement period. Use the worksheet below to calculate Tom and Barb's annual serial $($increasing$)$ savings requirement.

$(1)$ Determine the deflated value of the additional savings needed at retirement in today's dollars:

$$2,000,000$ Additional savings need at retirement

$\_25\_$ Number of periods until retirement

$\_4\%\_$ Inflation rate

Deflated value of additional savings need at retirement $$750,234$

$(2)$ Determine the amount that Tom and Barb need to save at the end of the first $($current$)$ year. This amount is increased each year during the pre$-$retirement period at the inflation rate.

$$750,234$ Deflated value of additional savings need at retirement $($from $(1))$

$----$ used as the future value to calculate the first serial $($increasing$)$ savings payment

$\_25\_$ Number of periods until retirement

$\_\_\_\_\_\_\%$ Inflation$-$adjusted yield using:

$\_7\%\_$ after$-$tax return

$\_4\%\_$ inflation rate

Formula: d $=([(1+$ i$)/(1+$ r$)]-1)$ X $100$

Calculate the first after$-$tax serial $($increasing$)$ savings payment before adjustment for inflation:

$$\_\_\_\_\_\_\_\_\_\_$

$(3)$ Inflation adjustment:

$\_\_\_\_\_\_\_$ First year unadjusted serial savings required $($from $(2))$:

$\_\_4\%\_\_$ Inflation rate:

FIRST YEAR SERIAL $($INCREASING$)$ SAVINGS AMOUNT ADJUSTED FOR INFLATION: $$\_\_\_\_\_\_\_\_\_\_$

Tom and Barb's first end$-$of$-$year savings payment, adjusted for inflation, is: