You have just turned 30 years? old, have just received your? MBA, and have accep
ID: 1171661 • Letter: Y
Question
You have just turned 30 years? old, have just received your? MBA, and have accepted your first job. Now you must decide how much money to put into your retirement plan. The plan works as? follows: Every dollar in the plan earns 9% per year. You cannot make withdrawals until you retire on your 70th birthday. After that? point, you can make withdrawals as you see fit. You decide that you will plan to live to 100 and work until you turn 70.You estimate that to live comfortably in? retirement, you will need $91,000 per year starting at the end of the first year of retirement and ending on your one hundredth birthday. You will contribute the same amount to the plan at the end of every year that you work. How much do you need to contribute each year to fund your? retirement?
Explanation / Answer
Amount required at the end of 70 Years is PV of future annuity
PV of ANnuity = CF * [ 1 - (1+r)-n ] / r
= $ 91000 * [ 1 - (1+0.09)-30 ] / 0.09
= $ 91000 * [ 1 - (1.09)-30 ] / 0.09
= $ 91000 * [ 1 - 0.0754] / 0.09
= $ 91000 * [ 0.9246 ] / 0.09
= $ 934873.3
Amount to be deposited every Year
FV of annuity = CF * [ (1+r)^n - 1 ] / r
934873.3 = CF [ ( 1+0.09)^40 - 1 ] / 0.09
= CF [ ( 1.09)^40 - 1 ] / 0.09
= CF [ ( 31.4094 - 1 ] / 0.09
= CF [ ( 30.4094 ] / 0.09
CF = 934873.3 * 0.09 / 30.4094
= $ 2766.86
Pls c
Pls comment, if any further assistance is required
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