Question

Peter wishes to create a retirement fund from which he can draw when he retires and the same amount at each anniversary of his retirement for years. He plans to retire years from now. What investment need he make today if he can get a return of per year, compounded annually

Answer 1

Answer:

$65,742.60

Explanation:

Note: The full question is "Peter wishes to create a retirement fund from which he can draw $20,000 when he retires and the same amount at each anniversary of his retirement for 10 years. He plans to retire 20 years from now. What investment need he make today if he can get a return of 5% per year, com- pounded annually?"

At first, we need to find the PV of withdrawals and there are 11 withdrawals starting 20 years from now.  

PV = PMT/r * 1 - 1/(1+r)^n. This formula gives the PV one period before the first withdrawal. That is 19 years from now because the first withdrawal is 20 years from now.

PMT = 20,000, n = 11,  

r = 0.05

PV19 = 20,000/0.05 * [1 - 1/(1+0.05)^11]

PV19 = 400,000 * 0.4153207109

PV19 = 166,128.28436

Now, we need to discount this back to toda

PV0 = PV19/(1 + r)^n; n = 19, r = 0.05

PV0 = 166,128.28436/(1 + 0.05)^1

PV0 = $65,742.6033421702

PV0 = $65,742.60

So, Peter needs to make $65,742.60 today.