Your friend is celebrating her 22nd birthday today and wants to start saving for her anticipated retirement at age 60. She estimates that the annual spending needs would be $210,000 based on the current price level, and inflation rate is expected to be 4% per year. She wants to be able to make withdrawal for spending needs on each year for 24 years following her retirement; the first withdrawal will be on her 61st birthday. Your friend intends to invest her money in a fund, which offers 5% percent interest per year after retirement. Before retirement, your friend invests in stock funds, which offers 9% interest per year. Your friend expects to spend $X for her wedding on her 30th birthday. She will get the $230,000 annual salary in 23rd birthday, and the salary is expected to be increased at 6%.
If she starts saving 20% of her salary on her 23rd birthday, up to 60th birthday, what is the maximum amount that she can spend on her wedding? Please list the formula and answer for the following figures.
Total amount required by her on 61st birthday = 210000 * 1.04 ^39 = $969436.86
Present value of spending needs after retirement in 60th birthday
=969436.86/1.05 + 969436.86*1.04/1.05^2+ ... + 969436.86*1.04^23/1.05^24
= 969436.86/1.05 * (1-(1.04/1.05)^24)/(1-1.04/1.05)
= $19,893,002.74
Present value of spending needs after retirement in 22nd birthday
= 19893002.79/1.09^38
= $ 752,477.33
First saving amount on 23rd birthday = 230000 * 20% = $46000, this amount will also increase by 6% per year
Present value of all savings in 22nd birthday
= 46000/1.09+ 46000*1.06/1.09^2+ ...... + 46000*1.06^37/1.09^38
=46000/1.09* (1-(1.06/1.09)^38)/(1-1.06/1.09)
=$1,002,384.67
Present value of amount which can be spent on wedding on 22nd birthday
= $1002384.67 - $752477.33 = $249907.34
Money that can spend on her wedding on 30th birthday
=$249907.34 *1.09^8
=$497956.02
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