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I have a econ midterm coming up soon and stumbled upon this question. My approach is:

2C=800/(1.12^2)+1200/(1.12^6)=125.71 or C=1245.71/2=622.85

But I have a gut feeling this is wrong. I believe the answer is somewhere around $781.

Consider the following cash flow diagram. What value of C makes the inflow series equivalent to the outflow series at an interest rate of 12% compounded annually?

enter image description here

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  • $\begingroup$ Are the C outflows a perpetuity (ie go on forever) $\endgroup$ – Kamster Feb 9 '15 at 2:09
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Interest rate is 12%, we'll assume some kind of simple day count scheme like 30/360.

Cash flows and discount factors for C payer

t   disc.fact.   rcv.cf  pay.cf  rcv.pv
0   1            0       -2C     0
1   .88          800     0       704
2   .7744        800     -C      619.52
3   .681472      800     -C      545.18
4   .59969536    800     -C      479.76
5   .527731916   1200    -C      633.28
6   .464404086   1200    -C      557.28
7   .408675596   1200    -C      490.41
8   .359634524   1200    -C      431.56

Receive total PV = 4,501.58

Pay total PV:

$$ \text{PayPV} = -2C -C.(1-0.12)^2 - C.(1-0.12)^3 .. \\ = -C \left(2 + \sum_{n=2}^{8} f^n \right) \\ = -C (5.816013485)$$

where $f=(1-0.12)$. Equate for Par:

$$ \text{RcvPV} + \text{PayPV} = 0\\ 4501.58 - 5.816013485 C = 0 \\ C = 774.00$$

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