The three year bond has face value $100, and pays \$5 coupons annually, the last one at maturity. Assume that the continuously compounding rate is 7%. The three year bond has face value USD 100, and pays USD 5 coupons annually, the last one at maturity. Assume that the continuously compounding rate is 7%.
(a) Find the price of this bond.
(b) Consider the investor who invests 1000 in these bonds. Each year after the coupon payments are issued, the investor buys the bonds from that money. What is the amount of money that the investor receives at the maturity of the bonds?
Is this correct for part a?
in class I learned bond price = $\frac{C}{1+r}+\frac{C}{(1+r)^2}+...+\frac{C+FaceValue}{(1+r)^2}$
where c = coupon payment and r = interest rate
$$\frac{5}{1+0.07}+\frac{5}{(1+0.07)^2}+\frac{105}{(1+0.07)^3} = 94.75$$
Is the correct price of the bond $\$94.75$?
For part b I don't understand what I have to do to solve the question?
 A: You are confusing compounding with continuously compounding. The former uses the 7% you have used. The latter would require you to calculate a compounded rate using 
(e^annual_rate)-1
Once you have that rate, you can use it in the formula you used.
On the second part:
At the end of each year, as the investor you'll get a lump sum of money - a coupon payment from each bond you bought at the beginning of the period.
Assuming you buy new bonds with the same features as your t0 bonds, at the end of year 2, you'll get money from t0 bonds held over the 2 year period AND the bonds you purchased at the end of year 1 etc.
So every year you hold the bonds you get coupons based on the compounded interest using the continuously compounded rate. You then buy more bonds with that money to add to your holding. At the end of the holding period, you get the last set of coupons (which you will not reinvest) and you also get the face value.
So:
At the end of year 1 you hold n-bonds.
At the end of year 1 you get n-bonds*coupon.
You then buy m-bonds
At the end of year 2 you hold n-bonds+m-bonds.
At the end of year 2 you get the coupon of year 2 on n-bonds + coupon of year 1 on n-bonds....
Coupon calculation as I described above.
Hope it helps.
Last point: when you buy a 3-year bond a year after issuance, you get a 2-year bond...etc.
