A bank owns a portfolio of bonds whose value P(r) depends on the interest rate r (measured in percent; e.g., r = 5 means a 5% interest rate). The bank’s quantitative analyst determines that

In finance, this second derivative is called bond convexity. Find the second Taylor polynomial of P(r) centered at r = 5 and use it to estimate the value of the portfolio if the interest rate moves to r = 5.5%.

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P(5) = 100,000, dP dr r=5 = -40,000, d²p| dr² = 50,000 =