Question

Question 1:

a. Your company is planning to borrow $2.5 million on a 3-year, 8%, annual payment, fully amortized term loan. What fraction of the payment made at the end of the second year will represent repayment of principal? Round your answer to two decimal places.

b. Assume that your aunt sold her house on December 31, and to help close the sale she took a second mortgage in the amount of $40,000 as part of the payment. The mortgage has a quoted (or nominal) interest rate of 10%, but it calls for payments every 6 months, beginning on June 30, and is to be amortized over 15 years. Now, 1 year later, your aunt must inform the IRS and the person who bought the house about the interest that was included in the two payments made during the year. (This interest will be income to your aunt and a deduction to the buyer of the house.) To the closest dollar, what is the total amount of interest that was paid during the first year?

Answer 1

Q1 a. Loan = 2.5 million = 2500000, Interest rate = 8% No of years = 3

First we need to find the annual payment of loan using PMT function in excel

Formula to be used in excel: =PMT(rate,nper,-pv)

Using PMT function in excel, we get Annual loan payment =$970083.7851

For year 1, Interest = Loan x interest rate = 2500000 x 8% = 200000, Principal payment for year 1 = Annual loan payment - Interest for year 1 = 970083.7851 - 200000 = 77083.7851, Ending loan balance for year 1 = Loan - Principal payment for year 1 = 2500000 - 77083.7851 = 1729916.2149

For year 2 , Ending loan balance for year 1 = Beginning loan balance for year 2 = 1729916.2149, Interest for year 2 = Beginning loan balance for year 2 x interest rate = 1729916.2149 x 8% = 138393.2971. Principal payment for year 2 = Annual loan payment - interest for year 2 =970083.7851 - 138393.2971 = 831690.4880

Fraction of payments that represents principal in year 2 = Principal for year 2 / Annual loan payment = $831690.4880 / 970083.7851 = 85.7338% = 85.73% (rounded to two decimal places)

Hence fraction of the payment made at the end of the second year that will represent repayment of principal = 85.73%

b. Mortgage or loan = $40000, No of half years in mortgage = 2 x no of years = 2 x 15 = 30

Semi annual interest rate = Nominal rate / 2 = 10% / 2 = 5%

First we will will find the semi annual payment of loan using PMT function in excel

Formula to be used in excel: =PMT(rate,nper,-pv)

Using PMT function in excel, we get Semi Annual loan payment =$2602.0574

For first six months of year 1 , Interest = Loan x semi annual interest rate = 40000 x 5% = 2000, Principal payment = Annual loan payment - Interest = 2602.0574 - 2000 = 602.0574, Ending loan balance for first six months of year 1 = Loan - Principal payment = 40000 - 602.0574 = 39397.9426

For second six months of year 1. Ending loan balance for first six months of year 1 = Beginning loan balance of second six months for year 1 = 39397.9426, Interest for year 2 = Beginning loan balance for year 2 x interest rate = 39397.9426 x 5% = 1969.8971

Total amount of interest paid during year 1 = Interest for first six months of year 1 + Interest for second six months of year 1 = 2000 + 1969.8971 = 3969.8971 = $3970 (rounded to closest dollar)

Hence,Total amount of interest paid during year 1 = $3970