$($ Financial Risk Management $)$

$3)$ A company holding a portfolio of hundreds of bonds practices cash flow mapping as part of their interest rate risk management. Consider the information in the table below:

$($Interest rate, $1$year $1\mathrm{.}25\%,2$years $1\mathrm{.}68\%),$

$($Volatility$,1$year $0\mathrm{.}25\%,2$years $0\mathrm{.}52\%),$

$($Cash$-$flows, $1$year $28,000,2$years $18,500).$

The company adds a new bond that makes a single payment of $1,300$ in $1\mathrm{.}5$ year$$s time. Calculate how the payment for this bond would be split between the existing payment bins. Assume that the correlation between variances is $0\mathrm{.}65.$