A borrower received a 30-year ARM mortgage loan for $200,000. Rate caps are 3/2/6. The start rate is 3.50% and the loan adjusts every 12 months for the life of the mortgage. The index used for this mortgage is MTA (for this exercise, 3.00% at the start of the loan, 4.45% at the end of the first year, and 4.50% at the end of the second year). The margin on the loan is 3.00%, which remains the same for the duration of the loan. What is the initial rate (start rate) the borrower will pay during the first year? What is the interest rate the borrower will pay after the first rate adjustment? (Hint: Remember to use the “stair step method” for determining the new interest rate.) What is the fully indexed rate after the second year? What is the maximum interest rate the borrower will pay during the 30-year term for this loan? If the interest rate is at its maximum, what would the MTA index have to be to reach the maximum interest rate?

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
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Chapter1: Investments: Background And Issues
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 A borrower received a 30-year ARM mortgage loan for $200,000. Rate caps are 3/2/6. The start rate is 3.50% and the loan adjusts every 12 months for the life of the mortgage. The index used for this mortgage is MTA (for this exercise, 3.00% at the start of the loan, 4.45% at the end of the first year, and 4.50% at the end of the second year). The margin on the loan is 3.00%, which remains the same for the duration of the loan.

  1. What is the initial rate (start rate) the borrower will pay during the first year?
  1. What is the interest rate the borrower will pay after the first rate adjustment? (Hint: Remember to use the “stair step method” for determining the new interest rate.)
  1. What is the fully indexed rate after the second year?
  1. What is the maximum interest rate the borrower will pay during the 30-year term for this loan?
  1. If the interest rate is at its maximum, what would the MTA index have to be to reach the maximum interest rate?
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An adjustable-rate mortgage is a house loan with a variable interest rate (ARM). An ARM's initial interest rate is fixed for a specific period of time. Following then, the interest rate applied to the outstanding debt is reset on a regular basis, at yearly or even monthly intervals. Variable-rate mortgages (ARMs) are sometimes known as floating mortgages. The interest rate on an ARM is adjusted depending on a benchmark or index, plus a spread known as an ARM margin. The London Interbank Offered Rate is the most common index used in ARMs (LIBOR).

Early in the loan period, payments are lower and rates are lower. People can purchase more costly homes than they otherwise might since lenders can take the reduced payment into account when determining the eligibility of borrowers. Borrowers can benefit from declining rates without refinancing thanks to it.

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