Question

Lisa Li is 36 years old today and plans to retire on her 60th birthday. With future inflation, Lisa estimates that she will require around S1,900,000 at age 60 to ensure that she will have a comfortable life in retirement. She is a single professional and believes that she can save S4,000 at the end of each month, starting in one months time and finishing on her 60th birthday i)If the fund to which she contributes her monthly saving of S4,000 eams 39% per annum, compounded monthly (after tax), how much will she have at age 60? Will she have achieved her targeted sum? What is the surplus or the shortfall? ii)When she reaches age 60, Lisa plans to travel extensively, and wishes to draw from her accumulated fund a monthly pension of S12,000, starting one month after her 60th birthday, and ending on her 65th birthday. She then wishes to draw a monthly pension starting one month after her 65th birthday, and ending on her 90th birthday, after which she expects that the fund will be fully expended If, after she reaches age 60, the fund continues to earn the above returm of 39% per annum, compounded monthly, calculate the monthly pension Lisa will be able to draw from the fund, starting one month after her 65th birthday. Assume that the fund balance reduces to zero as planned after the last pension payment is drawn on her 90th birthday

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B2 (i) retirement age current age no. of years remaining total monthly payments monthly payment annual rate monthly rate 36 288 4,000 3.90% 0.325% 10 balance in funds at retirement age balance required $ 1,902,640 $ 1,900,000 12 13 14 15 16 17 she will have achieved her targeted sum surplus 2,640 (ii) Present value of withdrawls made in 5 years $653,188.17 remaining present value for withdrawls that can be made for next 25 years $1,249,451.92 19 20 21 present value-annuity amount * present value annuity factor (0.325%, 300) the present value annuity factor used shall be the factor for 300 payments starting after 60 payments $1,249,451.92 annuity amount * 157.5811 annuity amount $1,249,451.92 /157.5811 23 annuity amount- $ 7,928.95 25 so, she can withdraw $7,928.95 pension per month starting one month after her 65th birthday till her 90th birthday 26 27

for formulas and calculations, refer to the images below -

B2 (i) retirement age 36 D2-D3 D4 12 current age no. of years remaining total monthly payments monthly payment annual rate monthly rate 0.039 D7/12 10 balance in funds at retirement age balance required -FV(D8,D5,D6,0,0) 1900000 12 13 14 15 16 17 she will have achieved her targeted sum surplus D10-D11 (ii) Present value of withdrawls made in 5 years -PV(D8,60,12000,0,0) remaining present value for withdrawls that can be made for next 25 years 18 19 20 21 -D10-D16 present value-annuity amount * present value annuity factor (0.325%, 300) the present value annuity factor used shall be the factor for 300 payments starting after 60 payments $1,249,451.92 annuity amount 157.5811 annuity amount $1,249,451.92 /157.5811 23 24 25 annuity amount- D18/L361 so, she can withdraw $7,928.95 pension per month starting one month after her 65th birthday till her 90th birthday 26

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