Suppose someone takes out a home improvement loan for $30,000. The annual interest on the loan is 6% and is compounded monthly. The monthly payment is $600. Let an denote the amount owed at the end of the nth month. The payments start in the first month and are due the last day of every month.

Give a recurrence relation for an. Don't forget the basis (also called the initial conditions).

Explanation:

Monthly interest = 6 / 12 = .005

principal amount a₀ = 30000

an denote the amount owed at the end of the month

amount owed at the end of one month

a₁= 1.005 x a₀ - 600

amount owed at the end of 2 nd  month

a₂= 1.005 x a₁ - 600

amount owed at the end of nth month

an =  1.005x an-1  - 600 for n ≥ 1

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