97. A combined bank loan and savings account can be modelled by two-input two-output difference equation...
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97. A combined bank loan and savings account can be modelled by two-input two-output difference equation 3-0 = [x₂[n+ 0 ABD+BIN where x₁ and x2 denote the balance of the loan account and savings account at the end of the n-th month; thus x₁ [0] and x2 [0] represent the initial values of the loan, and initial amount of the savings account. Also I₁ and 1₂ are the (annual) interest rates on the loan and savings accounts, respectively, while v₁ and v2 are the monthly payments on the loan and deposits into the savings account, made at the end of each month. Note: You may use MATLAB for the following calculations. 0 (a) Assume the initial amount in the savings account is $20,000, and assume monthly payments and deposits of p[n] = d[n] = $2,000. Assume interest rates of I₁ = 6% and 1₂ = 3%. Deter- mine the number of months required to pay off a loan of $300,000. (b) Determine the amount in the savings account at the end of this time. (c) Find the 'interest only' loan payment, i.e. the constant monthly payment v₁ [n] that will main- tain the loan balance at $300,000. (d) For the loan payment obtained in part (c), determine the smallest constant monthly deposit v₂[n] required to maintain the savings account balance at $20,000. 97. A combined bank loan and savings account can be modelled by two-input two-output difference equation 3-0 = [x₂[n+ 0 ABD+BIN where x₁ and x2 denote the balance of the loan account and savings account at the end of the n-th month; thus x₁ [0] and x2 [0] represent the initial values of the loan, and initial amount of the savings account. Also I₁ and 1₂ are the (annual) interest rates on the loan and savings accounts, respectively, while v₁ and v2 are the monthly payments on the loan and deposits into the savings account, made at the end of each month. Note: You may use MATLAB for the following calculations. 0 (a) Assume the initial amount in the savings account is $20,000, and assume monthly payments and deposits of p[n] = d[n] = $2,000. Assume interest rates of I₁ = 6% and 1₂ = 3%. Deter- mine the number of months required to pay off a loan of $300,000. (b) Determine the amount in the savings account at the end of this time. (c) Find the 'interest only' loan payment, i.e. the constant monthly payment v₁ [n] that will main- tain the loan balance at $300,000. (d) For the loan payment obtained in part (c), determine the smallest constant monthly deposit v₂[n] required to maintain the savings account balance at $20,000.
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Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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