- #1
issacnewton
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Homework Statement
The annually compounded discount rate is 5.5%. You are asked to calculate the present
value of a 12-year annuity with payments of $50,000 per year. Calculate PV for each of the
following cases.
a. The annuity payments arrive at one-year intervals. The first payment arrives one year
from now.
b. The first payment arrives in six months. Following payments arrive at one-year intervals
(i.e., at 18 months, 30 months, etc.).
Homework Equations
Annuity PV formula
The Attempt at a Solution
I have done the part a. I need help for part b. Let ##r = 0.055## and ##C = 50000##. The payments arrive at one-year intervals after the first payment which arrives in six months. So 11 payments will arrive at one-year intervals after the first payment which arrives in six months. PV of these payments at 6 month is given by the Annuity formula $$\mbox{PV } = 50000+\frac{C}{r} \left[ 1 - \frac{1}{(1+r)^{11}} \right]$$ So ##\mbox{PV } =
454626.8##. Now this is PV at 6 month. We want to convert this to today's value. ##r## here is annual rate. I want to convert this into equivalent monthly rate. For this, I did the following. Let ##r_m## be the equivalent monthly rate. Now $$P(1+r_m)^{12} = P(1+r)$$, where ##P## could be initial principal. So solving this for ##r_m##, we get, ##r_m = (1+r)^{1/12}-1##. So ##r_m = 0.00447169##. So discounting, the present value would be ##454626.8/ (1+r_m)^6 = $442617.70## But the answer is $442,603.98. So where have I gone wrong ?