Cheyenne wishes to endow a professorship at her alma mater. She learns that to d

Question

Cheyenne wishes to endow a professorship at her alma mater. She learns that to do so, she must contribute $1,000,000. What annual salary would a $1,000,000 gift support forever if salary payments are made monthly, starting one month after the gift, and the money's growth is governed by an annual effective discount rate of 6%?

I think after we compute the monthly interest rate into an annual interest rate
= (1+0.06/12)^12
= 1.061677812
>>> we get i(annual) = 0.061677812

>>> perpetuity = salary/i
>>> = salary/0.06161677812
and this value is = 1,000,000 - (1/12)salary since the payment is made one month after the gift???

so 16.21328594(salary) = 1,000,000 - (1/12)(salary)

which gives 16.2966129(salary) = 1,000,000
and gives a salary of 61362,42???

the actual salary is $62,035.20 which is given in the back of the book answer. Where did I go wrong??

Explanation / Answer

let the monthly salary be $ a.
for perpetual cash flow,
PV = a/k
so, a = PV*k
where, PV = present value = $ 1000000
and k = monthly interest rate = 6/12% = 0.005
a = 1000000*0.005 = $ 5,000 (ANSWER)

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