Over the past year (from one year ago to today), the inflation rate was 4.13%, the risk-free rate was 6.08%, and the real rate of return for a bond was 3.17%. The bond is currently priced at $974.00, pays annual coupons of $84.70, and just made a coupon payment. What was the price of the bond one year ago?
Real Return = 3.17%
Inflation Rate = 4.13%
Nominal Return = (1 + Real Return) * (1 + Inflation Rate) -
1
Nominal Return = (1 + 0.0317) * (1 + 0.0413) - 1
Nominal Return = 1.07431 - 1
Nominal Return = 0.07431 or 7.431%
Current Price = $974.00
Coupon = $84.70
Nominal Return = (Current Price + Coupon - Price 1 year ago) /
Price 1 year ago
0.07431 = ($974.00 + $84.70 - Price 1 year ago) / Price 1 year
ago
0.07431 * Price 1 year ago = $1,058.70 - Price 1 year ago
1.07431 * Price 1 year ago = $1,058.70
Price 1 year ago = $985.47
So, price of bond one year ago is $985.47
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