CFA CFA Level 1 Cash Flow Discounting (With Varying Spot Rates)

# Cash Flow Discounting (With Varying Spot Rates)

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I am not sure the way I ask the question will make sense but let me try…

I am wondering why when cash flows are discounted using different rates, that we square the 2nd period rate or cube the 3rd period rate instead of multiplying by previous rates. For example, if cash flows for each period are \$5, current spot rate for period 1 (discount rate) is 5%, spot rate for period 2 (discount rate) is 6%. I believe we would do \$5/1.05 + \$5/(1.06)^2 to figure out PV of these cash flows. What I am confused about is why we would do \$5/(1.06)^2 for the 2nd period instead of doing \$5/(1.05)(1.06) as the investor cannot earn 6% over the 2 periods just 6% in period 2 and 5% in period 1, yet we discount it back as if they could earn this 6% over both periods.

Anyone want to help out and explain to me what I am doing wrong/thinking of it wrong, that would be greatly appreciated!

Thanks