Edward intends to retire in 20 years. Upon retirement, he will require a yearly

Question

Edward intends to retire in 20 years. Upon retirement, he will require a yearly cash flow of $70,000 for 25 years to support his lifestyle (yearly cash flows assumed to occur at the end of each year). Anticipating his retirement plan, he started investing $6,000 per year five years ago and will continue to do so for 20 more years. How much more (over the current level of $6,000 pa) will Edward have to invest each year for the next 20 years to have the necessary funds for his retirement? Use a 10% per year discount rate throughout this problem (for discounting or compounding).

Explanation / Answer

To answer this question, we need to follow three steps. First, we need to calculate the present value of all the cash inflows for 25 years at the age of retirement. Second, we need to calculate the current value of the deposits of $6,000 every year. Lastly, we will calculate the required yearly deposits.

The Value of all cash inflows upon his retirement:

Present Value of an ordinary annuity: PV = Pmt x ((1-((1+r)-n )) / r)

Payment per period (PMT) = $70,000
Discount Rate per period= 10%
Number of periods (n) = 25

PV = $70,000 x ((1-((1+0.10)-25)) / 0.10) = $635,392.80

Current value of the deposits:

A = P((1+r)t-1) / r

where P is how much you put in the bank each period, r is the interest rate per period, t is the number of periods, and A is how much money you need in the future

($388,960.44*0.10) / ((1+0.10)20 – 1) = $6,791.10

So, the yearly deposits of $6,791.10 is required to get $70,000 per year after retirement.

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