Description of the activity and instructions

Our team has just opened Ceiling Street Bonds, an investment fund that invests only at a fixed rate and in which our family and friends have entrusted us several million euros. We have pre$-$selected some bonds that could be investments to have in the portfolio, but we want to analyze them more in depth.

First, we have US five$-$year bonds, issued on April $1,2020,$ and with a $1\%$ annual coupon. Second, there are the debt securities of Nordea, a Finnish private bank, due on August $18,2027,$ and with a coupon of $3\mathrm{.}75\%$ per year $($issued in dollars$).$ Finally, another option is JP Morgan bonds with a $3-$month LIBOR variable coupon plus $0\mathrm{.}25\%,$ which mature on December $31,2025.$ The discount rate for all public debt is $2\mathrm{.}5\%,$ while for private debt it is $3\mathrm{.}5\%.$ Likewise, the notional amount of all bonds is $$1000,$ and the current date is July $1,2023.$

Answer the following questions:

$$ What is the price of US Treasury bonds and Nordea bonds?

$$ What is the price of JP Morgan bonds, assuming that the $3$ month LIBOR remains constant at $4\%$ until maturity?

$$ How much does the accrued coupon of each bond amount to at the current date?

$$ What is the Macaulay duration, the modified duration of US Treasury bonds and the duration of the Nordea bonds?

$$ If the fixed discount rate depends on the $3$ month LIBOR, would the variable

coupon bonds last? Why?