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# How interest rate affects the mortgage value

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1. Consider a home mortgage where you borrow \$200,000 with a 30-year fixed rate loan. Suppose the mortgage interest rate is 0.708333% per month.
a. What is your monthly mortgage payment?
b. Solve for the principal and interest components of the first 12 mortgage payments. What is your outstanding mortgage balance at the end of the first year?
2. Consider the mortgage described in Question 1. Suppose 12 months have passed since the mortgage was issued and at the end of month 12, the interest rate on new mortgages is 0.75% per month.
a. What is the value of your mortgage?
b. Is the mortgage value above or below the mortgage balance? (Note: The mortgage balance was already calculated in 1(b). There is no need to recalculate this number.)
3. Consider the mortgage described in Question 1. Suppose 12 months have passed since the mortgage was issued and at the end of month 12, the interest rate on new mortgages is 0.66667% per month.
a. What is the value of your mortgage?
b) Is the mortgage value above or below the mortgage balance? (Note: The mortgage balance was already calculated in 1(b). There is no need to recalculate this number.)
4. (In this question, please keep as many digits as possible in all interim calculations. Any bit of rounding in the calculations used to answer part (a) is likely to lead to an error in part (b).)
Consider the mortgage described in Question 1. Suppose 12 months have passed since the mortgage was issued and at the end of month 12, the interest rate on new mortgages remains 0.708333% per month.
a) What is the value of your mortgage?
b) Is the mortgage value above or below the mortgage balance? (Note: The mortgage balance was already calculated in 1(b). There is no need to recalculate this number.)