Susan saved $5000 per year in her retirement account for 10 years (during age 25

Question

Susan saved $5000 per year in her retirement account for 10 years (during age 25-35) and then quit saving. However, she did not make any withdrawal until she turned 65 (i.e., 30 years after she stopped saving). Her twin sister, Jane did not save anything during the 1st 10 years (during age 25-30) but saved $5,000 per year for 30 years (during age 35-65). What will be the difference in their retirement account balance at age 65, if their investments earned an average return of 8% during the entire period?

Explanation / Answer

I = PTR / 100

susan savinga principle = 5000*10 = 50,000

susan interest =50,000*30*0.08 + 5000*(35 - 26)*0.08 + 5000(35 - 27) 0.08*..................*5000(35 - 35)0.08

susan interest =120,000+ 5000*0.08(9 +8+............................+1+0)

susan interest = 120,000 + 5000*0.08*(9*10/2)

susan interest = 120,000 + 5000*0.08*45

susan interest = 120,000 + 18,000

susan interest = $138,000

susan retirement account balance = 50,000+138,000 = $188,000

jane principle = 5000*30 = 150000

jane interest = 5000*0.08*( (65-36) + (65-37) +................+ (65-64) + (65 -65) )

Jane interest =  5000*0.08*( 29 + 28 +................+ 1 +0 )

Jane interest =  5000*0.08*( 29*30 /2)

Jane interest =  5000*0.08*( 29*30 /2)

Jane interest =  5000*0.08*( 29*30 /2)

Jane interest = $174,000

Jane account balance = 150,000 + 174000 = $324,000

difference in their retirement account balance at age 65 = 324000-188000 = $136000

and jane is having more money

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