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).

Question

Business

Babbles

17 March, 05:21

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).

+4

Answers (1)

Know the Answer?

Brenton Jackson · Answer 1

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