Question

1. You want to be able to withdraw 565,000 each year for 20 years during retirement. a. How much do you have to have saved to withdraw the $65.000 if the interest rate is 8%. b. You will achieve your goal by making monthly payments for 40 years. What does the monthly payment have to be to reach to goal you calculated in question 1? Rote 82 2. Determine the Price of the Bond at each time period. If you purchase the bond today (at time0) and hold it until maturity, what is the interest yield, capital gain yield, and total return the you will earn? Price Face Value Coupon Rate Discount Rate Time $1,000 Time Periods Remaining 8.00% 6.00% 3 years 3. Beans Corp just paid a dividend of S4.00. The dividend will grow at a rate of 15% for 2 years and then settle down to a more normal 6% growth rate, that will last indefinitely. If investors expect a 9% return on the stock what should the selling price be today?

Answer 1

1a.

We need to withdraw $65,000 each year for 20 years.
This is an annuity going for 20 years with an interest rate pf 8%

To know how much we should have saved, we should calculate the PV of this annuity at the beginning of retirement. I can be calculated using the following formula

$PV of annuity = P [\frac{1-(1+r)^{-n})}{r}]$

Substituting the values,

$PV of annuity = 65,000 [\frac{1-(1+0.08)^{-20})}{0.08}]$

Hence PV of annuity = $638,178

Hence we should have saved $638,178

b.

Now we know what should be the value of saving. We need to save this money for over 40 years by contributing every month. Which means we have 40*12 = 480 such periods of saving
Also, our interest rate is 8% annually, we need to consider a monthly interest rate. which will be calculated as 8%/12 = 0.67%

Hence using PV of annuity formula,

$638,178 = P [\frac{1-(1+0.0067)^{-480})}{0.0067}]$

$638,178 = P \times 143.2$

Hence P = $4,456.56

Hence $4,456.56 is the monthly payment to reach our goal