Upon retirement, your goal is to spend 3 years traveling around the world. To tr

Question

Upon retirement, your goal is to spend 3 years traveling around the world. To travel in style will require $50,000 per year at the beginning of each year. If you plan to retire in 25 years, what are the equal monthly payments necessary to achieve this goal? The funds in your retirement account will compound at 12% annually. Note that, there are 2 parts to this problem The Present Value of the annuity is PMT { (1 - 1/(1 + i/m)^N(m)]/N/m}_____________You payment amount is PMT { (1 + i/m)^N(m) - 1]/N/m}____________

Explanation / Answer

Funds required at the beginning of each year = $50000

No. of years of tour = 3

Interest rate = 12%

Thus,

Present value of all 3 year fund at the beginning of the tour= 50000 + 50000/(1+R) +50000/(1+R)^2

Present value of all 3 year fund at the beginning of the tour= 50000 + 50000/(1+12%) +50000/(1+12%)^2

Present value of all 3 year fund at the beginning of the tour= $134502.55

Now,

Monthly payment to become the future value of $134502.55 is P

Thus,

134502.55 = P*((1+1%)^300 – 1) / .01 = P*1878.85

P = 134502.55/1878.85

P = 71.59

2.

Present value of annuity = 71.59*(1-1/1.01^300)/.01   =$6797.22

3.

Future value of payment = = P*((1+1%)^300 – 1) / .01 = 71.59*((1+1%)^300 - 1) / .01 = $134506.63

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