Question

q1.

What is the price of a 14-year bond paying 9.1% annual coupons with a face (par) value of $1,000 if the market rates for these bonds are 5.5%? Answer to the nearest cent, xxx.xx, and enter without the dollar sign.

q2.

You are borrowing $200,000 for an amortized loan with terms that include annual payments,6 year loan, and interest rate of 7.2 per year. How much of the first year's payment would be applied toward reducing the principal?

Answer 1

Question 1:

n = 14 years

C = Coupon payment = $1,000 * 9.1% = $91

r = market rate = 5.5%

Face Value = $1,000

Price of bond = [C*[1 - (1+r)^-n]/r] + [Face Value / (1+r)^n\

= [$91 * [1 - (1+5.1%)^-14] /5.1%] + [$1,000 / (1+5.1%)^14]

= [$91 * 0.501618428 / 0.051] + [$1,000 / 2.00649473]

= $895.044645 + $498.381573

= $1,393.42622

Therefore, price of bond is 1,393.43

Question 2:

Loan Amount = $200,000

n = 6 years

r = interest rate = 7.2%

Annual Loan payment = [r*PV] / [1 - (1+r)^-n]

= [7.2%*$200,000] / [1 - (1+7.2%)^-6]

= $14,400 / 0.341082127

= $42,218.571

Annual loan payment is $42,218.57

Interest on loan for 1st year = Outstanding amount * interest rate = $200,000*7.2% = $14,400

First year payment to be applied toward reducing principal = Annual loan payment - Interest on loan for 1st year

= $42,218.57 - $14,400

= $27,818.57

Therefore, first year payment to be applied toward reducing principal is $27,818.57