Zadanie z kredytem Janek: Imagine you have e300000 to invest, at a constant rate of 7%, and that you want to withdraw a fixed amount I at the end of each year for next fifteen years. What is the maximum possible value of I for which this is possible?

Trivial: K₀ = 300 000 K_n+1 = mK_n − I, m = 1.07 K₁₅ = 0. Now just solve for I.

Thoms: możesz rozpisać jak?

Trivial: K_n = mK_n−1 − I K_n = m²K_n−2 − mI − I K_n = m³K_n−3 − m²I − mI − I ... K_n = mⁿK₀ − mⁿ⁻¹I − ... − m²I − mI − I K_n = mⁿK₀ − I(1 + m + m² + ... + mⁿ⁻¹)

	mn−1
Kn = mnK0 − I
	m−1

	m−1
I =		(mnK0 − Kn)
	mn−1

dla n = 15 mamy K_n = K₁₅ = 0 czyli:

	m−1
I =		m15K0 = 32938.387410301958954654293081504...
	m15−1