Variable yield curve

We are only given the 1 year, 5 year and 10 year yield curve values, and have to guess what the remaining values should be. Without further data, the best estimate of the 2, 3, 4 year yield rate would be the 5 year yield rate, and the 6, 7, 8 year yield rate would be the 10 year yield rate.

As such, this gives us the following table:

In the wiki, there is a formula that states: $\small PV = \frac{ c\% \$P } { ( 1 + y_1 \% ) ^ 1 } + \frac{ c\% \$P } { ( 1 + y_2 \% ) ^ 2 } + \frac{ c\% \$P } { ( 1 + y_3 \% ) ^ 3 } + \ldots + \frac{ c\% \$P } { ( 1 + y_{T-1} \% ) ^ {T-1} } + \frac{ c\% \$P + \$P} { ( 1 + y_T \% ) ^ T }.$

The industrial standard is to use the data for the year that is available next whenever some particular value is not available (even though that might not be the best way to approximate it.

$\frac{0.1 \times 1000+1000}{(1+0.03)^{10}}+\frac{0.1 \times 1000}{(1+0.005)^1}+\frac{0.1 \times 1000}{(1+0.0075)^2}+\frac{0.1 \times 1000}{(1+0.0075)^3}+\frac{0.1 \times 1000}{(1+0.0075)^4}+\frac{0.1 \times 1000}{(1+0.0075)^5}+\frac{0.1 \times 1000}{(1+0.03)^6}+\frac{0.1 \times 1000}{(1+0.03)^7}+\frac{0.1 \times 1000}{(1+0.03)^8}+\frac{0.1 \times 1000}{(1+0.03)^9}$

Mathematica Code:

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In[62]:= (0.1 1000/(1 + 0.005)^1 + ((0.1) 1000)/(1 + 
   0.0075)^2 + ((0.1) 1000)/(1 + 0.0075)^3 + ((0.1) 1000)/(1 + 
   0.0075)^4 + ((0.1) 1000)/(1 + 0.0075)^5 + ((0.1) 1000)/(1 + 
   0.03)^6 + ((0.1) 1000)/(1 + 0.03)^7 + ((0.1) 1000)/(1 + 
   0.03)^8 + ((0.1) 1000)/(1 + 0.03)^9 + ((0.1) 1000 + 
  1000)/(1 + 0.03)^10

Out[62]= 1628.33