Question

Question 2

You decide to borrow $250,000 to build a new home. The bank charges an interest rate of 5% compounded monthly. If you pay back the loan over 30 years, what will your monthly payments be (rounded to the nearest dollar)?

		$1,687
		$1,499
		$1,834
		$1,342

Question 9

Last year, you bought a bond with face value $1000, maturity 15 years, coupon rate of 5.5% per year payable semi-annually and yield to maturity of 7% per year. Currently the bond sells for $900. How much would be your total yield if you sell this bond today?

		13.71%
		10.78%.
		(17.84%)
		(15.79%)

Answer 1

Answer to Question 2:

Amount borrowed = $250,000
Annual interest rate = 5%
Monthly interest rate = 0.4167%
Period = 30 years or 360 months

Let monthly payment be $x

$250,000 = $x/1.004167 + $x/1.004167^2 + .... + $x/1.004167^359 + $x/1.004167^360
$250,000 = $x * (1 - (1/1.004167)^360) / 0.004167
$250,000 = $x * 186.2731343
$x = $1,342

Monthly payment = $1,342

Answer to Question 9:

Calculation of purchase price:

Par value = $1,000

Annual coupon rate = 5.50%
Semiannual coupon rate = 2.75%
Semiannual coupon = 2.75% * $1,000
Semiannual coupon = $27.50

Time to maturity = 15 years
Semiannual period = 30

Annual YTM = 7.00%
Semiannual YTM = 3.50%

Price of Bond = $27.50 * PVIFA(3.50%, 30) + $1,000 * PVIF(3.50%, 30)
Price of Bond = $27.50 * (1 - (1/1.035)^30) / 0.035 + $1,000 / 1.035^30
Price of Bond = $862.06

Total Yield = (Selling price + Coupons received - Purchase price) / Purchase price
Total Yield = ($900 + $55 - $862.06) / $862.06
Total Yield = 10.78%