Calculating YTM of Coupon Bond based on Information from Zero Coupon Bonds

[furnishowma]

The following table summarizes prices of various risk-free, zero-coupon bonds (expressed as a percentage of face value, per $100 face value):
Maturity (years)
1: $95.51
2: $91.05
3: $86.38

The YTM are as follows
1-year: 4.7%
2-year: 4.8%
3-year: 5%

Given this information, what’s the YTM of a three-year risk-free bond with 5% coupon rate and annual coupons?

For me, I assume that the coupon payment is $100. So since 5% is $100, 100% is $2,000 which is the face value of the bond.
So the price of the bond is $100/(1+4.7%) + $100/(1+4.8%)^2 + 2100/(1+5%)^3 which equals to $2000.62

Using trial and error to get the YTM of the bond, the YTM is 5%.

Is this the correct way of doing it? How would you do it?

 

[Deleted member 4993]

The following table summarizes prices of various risk-free, zero-coupon bonds (expressed as a percentage of face value, per $100 face value):
Maturity (years)
1: $95.51
2: $91.05
3: $86.38

The YTM are as follows
1-year: 4.7%
2-year: 4.8%
3-year: 5%

Given this information, what’s the YTM of a three-year risk-free bond with 5% coupon rate and annual coupons?

For me, I assume that the coupon payment is $100. So since 5% is $100, 100% is $2,000 which is the face value of the bond.
So the price of the bond is $100/(1+4.7%) + $100/(1+4.8%)^2 + 2100/(1+5%)^3 which equals to $2000.62

Using trial and error to get the YTM of the bond, the YTM is 5%.

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Calculate Two-year Risk-free Interest Rate

Given the following information from the market: the six-month risk-free interest rate is 2% (for six months); the YTM of a one-year risk-free bond with 8% coupon rate (APR) and semiannual coupons is 6% (APR); the YTM of a two-year risk-free bond with 10% coupon rate and annual coupons is 5%...

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[JeffM]

You can represent the cash flows on the 5% coupon bond with a face value of 100 as
5 at the end of year 1
5 at the end of year 2
105 at the end of year

Now what?