The yield of this type of bond is similar to cash flow analysis, in the sense that there is an initial expenditure, i. e., the purchase price of the bond, which is taken per hundred, or $100.00. Then you have 5 annual positive cash flows of: $5, $6, $7, $8, $9 plus the return of the par value of the bond in the 5th year, or $100.
We simply find the PV of each year's cash flow using: PV=FV(1 + R)^-N, for each year, and then add them all up to see how close they come to the purchase price of $100.00. We assume an initial yield of 7%, which is the average of the 5 cash flows. This gives an NPV of $99.45, which is a bit too high. If we try 6.75%, it gives an NPV of $100.49, which is little too low. Interpolation between these values gives a very accurate yield of: 6.86741572077%.........., which is the yield of this savings bond.
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