Review the following computation for part a and b.

Your part (a) here is another way to solve for part a / b:

$20,000 (1/1.06)^12 = $20,000 x .4970 = $9,940or $20,000 (1.06)^12 = $20,000 / 2.0122 = $9,939.37 rounding (part-a)

Part b See the example below

Determining the present value of a perpetuity using your data

PMT x (1 / R) Part (b) Pmt = Present value of Annuity divided by (Future value Interest Factor annuity at r, n)

$5,000 x (1/.06) = $5,000 x 16.6667 = $83,334 how large must the endowment be.

PMT = Present value annuity divided Future value interest factor annuity at 6%, 50 years. (I used the future annuity table)

Pmt = $83,334 / 290.336 = $287.02 per yr. for the next 50 years.

Additional question:

You wish to purchase a home in five years from now and estimates that an initial down payment of $20,000 will be required at that time; and you wish to make equal annual end-of year deposits in an account paying annual interest of 4 percent, so what size annuity will result in a lump sum equal to $20,000 at the end of year 5.