You have just purchased a home by borrowing $400,000 for 30-years at a fixed APR of 3.87%. The loan payments are monthly and interest is compounded monthly. a. What is the periodic interest rate? (I. e., what is the monthly interest rate?) b. What is the effective annual rate on the loan? (I. e., what is the interest rate once we take into account compounding?) c. What is the monthly mortgage payment?

Question

Alicia White

Business

2 May, 09:09

You have just purchased a home by borrowing $400,000 for 30-years at a fixed APR of 3.87%. The loan payments are monthly and interest is compounded monthly. a. What is the periodic interest rate? (I. e., what is the monthly interest rate?) b. What is the effective annual rate on the loan? (I. e., what is the interest rate once we take into account compounding?) c. What is the monthly mortgage payment?

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Answers (1)

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Jayden Haley · Answer 1

a. 0.3225% per month

b. 3.9393874%

c. $1,879.80

Explanation:

a. 3.87%/12

= 3.87/100

= 0.0387/12

= 0.003225 * 100

= 0.3225% per month

b. (1 +.003225) ^12 - 1

= 1.039393874 - 1 =.039393874

= 3.9393874% (note how this is slightly larger than 3.87%)

c. The formula to solve this is P r / (1 - ((1 / (1+r)) ^n)

$400,000 *.003225 / (1 - ((1 / (1+.003225)) ^360) = $1,879.80