Susan and Jeff each make deposits of 100 at the end of each year for 40 years. Starting at the end of the 41st year, Susan makes annual withdrawals of X for 15 years and Jeff makes annual withdrawals of Y for 15 years. Both funds have a balance of 0 after the last withdrawal. Susan's fund earns an annual effective interest rate of 8%. Jeff's fund earns an annual effective interest rate of 10%. Calculate ( Y − X ) .

$2,792.38

Explanation:

According to the scenario, computation of the given data are as follow:-

For computing the difference, first we have to compute the future value after that PMT value should be find out

Future value = PMT ×  FVIFA

FVIFA = [(1 + interest rate)^number of years - 1] ÷ interest rate

For S

PMT = $100

Time = 40 years

Rate = 8% = 0.08

Future value of Susan = $100 × FVIFA (0.08)40

= $100 × 259.057

= $25,905.7

For J

PMT = $100

Time = 40 years

Rate = 10% = 0.10

Future value of Jeff=100 × FVIFA (0.10)40

= $100 × 442.593

= $44,259.3

Future value of Deposit made by Susan = $25,905.7  

Future value of Deposit made by Jeff = $44,259.3

Annual withdraw by X and Y:-  

Now PMT is

PMT = PV ÷ PVIFA  

PVIFA = [1-1 ÷ (1 + interest rate)^number of years] ÷ interest rate

Present value of Susan= $ 25,905.7

Time = 15 years

Rate = 8% = 0.08

PMT= $25,905.70 ÷ 8.5595 = $3,026.54

Present value of Jeff = $44,259.3

Time = 15 years    

Rate = 10% = 0.10

PMT=$44,259.3 ÷ 7.6061 = $5,818.92

Payment of Susan (X) = $3,026.54

Payment of Jeff(Y) = $5,818.92

Difference between Susan(X) and Jeff(Y) is

=  Payment of Jeff(Y) - Payment of Susan(X)

= $5,818.92 - $3,026.54  

= $2,792.38

answer; limited pay life;

answer; false pretense;