Assume that you have 40 years until retirement and have just started your first

Question

Assume that you have 40 years until retirement and have just started your first job. Once you retire, you anticipate that you will live for 30 additional years. Assume that you will require $100,000 per year to support yourself in retirement. All investments that you make will go into and stay in an account that returns 6% per year (i.e. however much you have at retirement will sit in that account and continue to accrue interest on the remaining balance.) How much will you have to save each year over the next 40 years to meet your goal? Assume that your first investment occurs at the end of your first year of work (yr 1) and that the last of your 40 investments occurs on the last day that you are employed (yr 40). For simplicity, assume that your first withdrawal is at the end of your first retirement year (yr 41).

Explanation / Answer

First we find the amount we need at start of41 year in the account

FV is 0, coupon is 100,000, yield us 6%, N is30

So value that must be in account is 1,376,483.11

Now we find how much need to be deposited each year

N is 40, FV is 1,376,483.11 , yield is 6%, PV is 0

So coupon is 8894.19$ per year must be deposited

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