ES3083 Test 1 Problems 14 are multiplechoice problems 10poi

ES-3083 Test # 1 Problems 1-4 are multiple-choice problems, 10-point each. To obtain the full credit, you must show the work that leads to the answer. 1. An interest rate of 15% per year, compoundedmonthl) is nearest to (a) 1 .00% per month (b) 15.12% per year (c) 16.08% per year (d) 16.93% per year 2. You purchase a $10,000 bond with a bond rate of 6% per year payable semiannually and sell at face value after 2 years. You pay $9,600 for the bond. Which statement is correct? (a) Semiannual cash flows will be -$9600, $300, $300, 5300, S9700 and the bond will earn (b) Semiannual cash flows will be -$9600, $300, $300, $300, $9700 and the bond will earn (c) Semiannual cash flows will be -$9600, $300, S300, $300, S10,300 and the bond will earn (d) Semiannual cash flows will be -$9600, $300, 5300, $300, $10,300 and the bond will earn more than 10% less than 10% more than 10% less than 10%

Solution

1) Here the compounding frequency is 12 as the compounding is monthly

So, Net interest rate per year = (1 + 15%/12)^1*12 - 1 = 1.0125¹² - 1 = 16.08%

Ans: 16.08% per year (Option C)\\

2) Face Value of the bond = $10,000

PV of the bond = $9600

Number of periods = 2*2 = 4 (because this is a semiannual bond)

PMT (Payment per period) = 6%/2 * $10,000 = $300

In case of a bond an investor initially pays the price of the bond and then gets coupon payments every period and for the last period he gets the coupon payment plus the face value of the bond.

So, the cash flows will be -$9600, $300, $300, $300, $10,300

Using RATE function in excel to calculate the rate earned:

RATE =RATE(4,300,-9600,10000,0)*2 = 8.21%

Ans: Option D