Question

# 3. You take a \$500,000 mortgage to buy a vacation home. The mortgage entails equal monthly...

3. You take a \$500,000 mortgage to buy a vacation home. The mortgage entails equal monthly payments for 10 years, 120 payments in all, with the first payment in one month. The bank charges you an interest rate of 9.6% (APR with monthly compounding).

a. How much of your first payment is interest, and how much is repayment of principal?

b. What is the loan balance immediately after the 10th payment? (Calculate the loan balance using the annuity formula.)

c. How much of your 10th payment is interest, and how much is repayment of principal?

a.

Calculating Monthly Payment,

Using TVM Calculation,

PMT = [PV = 500,000, FV = 0, N = 120, I = 0.096/12]

PMT = \$6,497.28

Interest = (0.096/12)500,000 = \$4,000

Principal = 6,497.28 - 4,000 = \$2,497.28

b.

Calculating Loan Balance after 10th payment,

Using TVM Calculation,

FV = [PV = 500,000, PMT = -6,497.28, N = 10, I = 0.096/12]

FV = \$474,108.73

c.

Calculating Loan Balance after 9th payment,

Using TVM Calculation,

FV = [PV = 500,000, PMT = -6,497.28, N = 9, I = 0.096/12]

FV = \$476,791.68

Interest Paid in 10th payment = (0.096/12)(476,791.68) = \$3,814.33

Principal Paid in 10th payment = 6,497.28 - 3,814.33

Principal Paid in 10th payment = \$2,682.95

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