Question

15. What are the proceeds of $1,000,000 deposited in a bank yesterday (Aug 6) for 1 month at 1.5%? Take care to apply “money market” rules and use the proper “day count.”

16. What is the present value (as of today, Aug 7) of $1MM to be paid Feb 7 2019 at a (discount) rate of 2%. (Same instructions as in 15.)

17. An asset promises to pay the following:

? $60 each year for the next ten years: and

? $1,000 in ten years

Assume all the cash flows are discounted by 6%. Use the annuity formula to get the price of the first part. Use the standard discounting formula to get the price of the second part. Add them together. This is a bond with a coupon rate of 60/1,000 = 6% and a maturity of ten years. Its yield-to-maturity is 6%.

18. Consider a bond with a coupon rate of 5%, face value $100,000 and twenty year maturity.

?a) What is its price if the yield-to-maturity is 5%? What about 6%? 4%? Calculate these as ?explained in #17, or use the bond pricing formula.

?b) Repeat the three parts of a) but for a thirty-year maturity.

Answer 1

15	1000000*30/360*1.5%
	1250
Proceeds from investment = (1000000+1250)					1001250	$1,001,250
16	1000000*(1/(1.02^(60/360)))
	996705
The present value would be $ 996705
17	Annuity factor = (1-(1+r)^-n)/r
		(1-(1+0.06)^(-10))/0.06
		7.3601
	Present value of $ 60 received for next ten years
	$60*7.3601		441.606
	Present of $ 1000
	1000*(1/(1.06^10))
	1000*0.558395		558.395
	Price of Bond		$1,000
18	If yield to maturity is 5%
	Annuity factor = (1-(1+r)^-n)/r
		(1-(1+0.05)^(-20))/0.05
		12.4622
	Present value of $ (100000*5%) = $ 5000 received for next 20 years
	$5000*12.4622		62311
	Present of $ 1000
	100000*(1/(1.05^20))
	100000*0.376889		37688.9
	Price of Bond		$100,000
	If yield to maturity is 6%
	Annuity factor = (1-(1+r)^-n)/r
		(1-(1+0.06)^(-20))/0.06
		11.4699
	Present value of $ (100000*5%) = $ 5000 received for next 20 years
	$5000*11.4699		57349.5
	Present of $ 1000
	100000*(1/(1.06^20))
	100000*0.311805		31180.5
	Price of Bond		$88,530
	If yield to maturity is 4%
	Annuity factor = (1-(1+r)^-n)/r
		(1-(1+0.04)^(-20))/0.04
		13.5903
	Present value of $ (100000*5%) = $ 5000 received for next 20 years
	$5000*12.5903		62951.5
	Present of $ 1000
	100000*(1/(1.04^20))
	100000*0.456387		45638.7
	Price of Bond		$108,590
18	If maturity is 30 years
	Annuity factor = (1-(1+r)^-n)/r
		(1-(1+0.05)^(-30))/0.05
		15.37245
	Present value of $ (100000*5%) = $ 5000 received for next 20 years
	$5000*15.37245		76862.25
	Present of $ 1000
	100000*(1/(1.05^30))
	100000*0.231377		23137.7
	Price of Bond		$100,000
	If yield to maturity is 6%
	Annuity factor = (1-(1+r)^-n)/r
		(1-(1+0.06)^(-30))/0.06
		13.76483
	Present value of $ (100000*5%) = $ 5000 received for next 20 years
	$5000*13.76483		68824.15
	Present of $ 1000
	100000*(1/(1.06^30))
	100000*0.17411		17411
	Price of Bond		$86,235
	If yield to maturity is 4%
	Annuity factor = (1-(1+r)^-n)/r
		(1-(1+0.04)^(-30))/0.04
		17.29203
	Present value of $ (100000*5%) = $ 5000 received for next 20 years
	$5000*17.29203		86460.15
	Present of $ 1000
	100000*(1/(1.04^30))
	100000*0.308319		30831.9
	Price of Bond		$117,292