Question

3. Interest Rates You have just purchased a home and taken out a $460,000 mortgage. The mortgage has a 30-year term with monthly payments and an APR of 6.08%. a. How much will you pay in interest, and how much will you pay in principal, during the first year? b. How much will you pay in interest, and how much will you pay in principal, during the 20th year (i.e., between 19 and 20 years from now)?

Answer 1

(5) Mortgage = $ 460000, Tenure = 30 years and APR = 6.08%

Applicable Monthly Rate = 6.08 / 12 = 0.5067 %

Let the monthly repayments be $ K

Therefore, 460000 = K x (1/0.005067) x [1-{1/(1.005067)^(360)}]

460000 = K x 165.3632

K = 460000 / 165.3632 = $ 2781.75

(a) Mortgage Outstanding at the end of Year 1 = 2781.75 x (1/0.005067) x [1-{1/(1.005067)^(348)}] = $ 454435.4014

Principal Paid in First Year = 460000 - 454435.4014 = $ 5564.598

Interest Paid in Year 1 = 12 x 2781.75 - 5564.598 = $ 27816.46

(b) Mortgage Outstanding at the end of Year 19 = 2781.75 x (1/0.005067) x [1-{1/(1.005067)^(12)}] = $ 32307.14866

Principal Repaid in Year 20 = 32307.14866

Interest Paid in Year 20 = 2781.75 x 12 - 32307.14866 = $ 1073.911

NOTE: Please raise a separate query for the solution to the second unrelated question as one query is restricted to the solution of only one complete question with up to four sub-parts.