Question

19) You are in need of a personal loan for $3,000 to be returned after 3 years. Bank A offers you the loan at yearly interest of 12% compounded monthly, while Bank B offers you the loan at yearly interest of 12.5% compounded quarterly. You prefer the offer from Bank ______ ; because the future value (FV) of $______ is less than (FV) of $______. 20) Which of the following (one-year) $6,000 face-value securities has the highest yield to maturity? A) A 5 percent coupon bond selling for $4,000 B) A 10 percent coupon bond selling for $4,500 C) A 9 percent coupon bond selling for $6,000 D) A 6 percent coupon bond selling for $6,500 E) A 11 percent coupon bond selling for $4,300 21) Which of the following (one-year) $6,000 face-value securities has the lowest yield to maturity? A) A 5 percent coupon bond selling for $4,000 B) A 10 percent coupon bond selling for $4,500 C) A 9 percent coupon bond selling for $6,000 D) A 6 percent coupon bond selling for $6,500 E) A 11 percent coupon bond selling for $4,300 22) A $6,000 bond has a coupon rate of 6% and 4 years to maturity. If interest rates rise from 6% to 30%, its rate of return to maturity is:

show your work

Answer 1

19)

Bank A : Amount after 3 years = = 4292

Bank B : Amout after 3 years = = 3957

Thus, bank B is preffered. Future value of 3957 < 4292

20)

Time period = 1 year, face value = 6000

YTM = r

A : 4000 = , r = 57.5%

B : 4500 = , r = 46.6%

C : 6000 = , r = 9%

D : 6500 = , r = -2%

E : 4300 = , r = 53.5%

Security A has highest YTM

21)

Same securities as 20. Thus same calculations.

Security D has lowest YTM

22)

The question doesnt mention when the rate of interest is changing. If rate changes at t = 1 , yield to maturity will be same as interest, i.e 30%.

If rate changes in year t , following is the method:

Coupon = 6000 x 0.06 = 360
Time left = 4-t years.

Initial bond value = where n goes from 1 to 4

Bond value at t = where n goes from t to 4 .

Let new YTM be r .

then : Initial bond value  = where n goes from 1 to t.

Solving for r gives YTM. Solve according to t.

If rate changes at t = 1 , yield to maturity will be same as interest, i.e 30%.