WITHOUT USING THR FINACIAL CALCULATOR OR EXCEL
2. Gary Luff is trying to plan for retirement in 10 years, and currently he has $150,000 in a savings account and $250,000 in shares. In addition, he plans on adding to his savings by depositing $8,000 per year in his savings account at the end of each of the next five years and then $10,000 per year at the end of each year for the final five years until retirement. Required:
(a) Assuming Gary’s savings account returns 8% compounded annually while his investment in shares will return 12% compounded annually, how much will he have at the end of 10 years? (Ignore taxes).
(b) If Gary expects to live for 20 years after he retires, and at retirement he deposits all of his savings in a bank account paying 11%, how much can he withdraw each year after retirement (20 equal withdrawals beginning one year after he retires) to end up with a zero balance at death?
a] | FV of amount in shares = 250000*1.12^10 = | $ 7,76,462 |
FV of the amount in savings account today = 150000*1.08^10 = | $ 3,23,839 | |
FV at EOY 10 of the annual deposits of $8000 per year from EOY 1 to EOY 5 = 8000*(1.08^5-1)*1.08^5/0.08 = | $ 68,960 | |
FV at EOY 10 of the annual deposits of $10000 per year from EOY 6 to EOY 10 = 8000*(1.08^5-1)/0.08 = | $ 46,933 | |
Amount Gary will have in total at EOY 10 | $ 12,16,193 | |
b] | The above amount is the PV of the 20 annual | |
equal withdrawals that he is going to make. | ||
Using the formula for finding PV of annuity, | ||
1216193 = A*(1.11^20-1)/(0.11*1.11^20) | ||
where A = the annual withdrawals | ||
Therefore, A = 1216193*0.11*1.11^20/(1.11^20-1) = | $ 1,52,724 |
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