Question

In: Economics

9. Calculate the value of the following loans. Assume a face value of $100,000 and that...

9. Calculate the value of the following loans. Assume a face value of $100,000 and that the yield to maturity on each is 6%. All interest rates are stated as annual rates.

a. a 3-year interest only mortgage with a coupon rate of 6.75%, monthly payments of interest, and the entire principal repaid at maturity.

b. a 10-year, fully amortized mortgage with quarterly payments and an interest rate of 4.75%.

10. Calculate the duration of each loan from question 9.

Solutions

Expert Solution

9)

a)

The value of the loan is calculated using the following equation

Value of the loan = $ 102,054.44

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b)

The quarterly payment on the loan is calculated as follows

Quarterly payment = $3,155.12

The value of the loan is the present value of the quarterly payment discounted at the yield to maturity of 6% , compounded quarterly.

The present value is calculated as follows:-

Value of the loan = $ 94,388.08

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10)

In the case of a, the duration of the loan is 36 months or 3 years.

In the case of b, the duration of the loan is 40 quarters or 10 years.

Rahul Sunny answered 2 years ago
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