You are trying to plan for retirement in ten years and currently you have $10000

Question

You are trying to plan for retirement in ten years and currently you have $100000 in savings account and $300000 in shares. In addition you plan on adding to your savings by depositing $10000 per year in your savings account at the end of each of the next 5 years and then $20000 per year at the end of each year for the final years until retirement.
a) assuming your saving account returns 7% compounded annually while your investment in shares will return 12% compounded annually,how much will you have at the end of ten years(ignore taxes)
b) if you expect to live for 20 years after you retire and at the retirement you deposit all your savings in a bank account paying 10%, how much can you withdraw each year after retirement to end up with zero balance at the death??

Explanation / Answer

a)
At the end of 10 years,
FV of savings
= 100000*1.07^10 + 10000(1.07^9 +.....!.07^5) + 20000*(1.07^5-1)/0.07
= 196715 + 10000*1.07^5*(1.07^5-1)/0.07 + 20000*(1.07^5-1)/0.07
= 196715 + 80657 + 115015
= 392387 ($)
FV of returns on shares = 300000*1.12^10 = 931754 ($) (rounded off to nearest $)
Total amount at the end of 10 years = 392387 + 931754 = 1324141 ($) (ANSWER)
b)
let a be the amount to be drawn every year.
Then, a*1.1(1.1^20-1)/0.1 = 1324141*1.1^20
= 1324141*1.1^20*0.1/(1.1*(1.1^20-1))
= 141394 ($) (rounded off to nearest $) (ANSWER)

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