# Cash flow diagram, interest rate inflow series

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? • Are the C outflows a perpetuity (ie go on forever) – Kamster Feb 9 '15 at 2:09 ## 1 Answer 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:

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