An index$-$linked bond of $11,000$ nominal was issued on $1^{5t}$ July $2016$ and it was repaid at $114\%$ on $7^{st}$ July $2020.$ Interest on the bond was payable at each anniversary $($i$.$e$.$ in July of each year$)$ at a rate of $5\mathrm{.}1\%$ per annum.

An investor liable to income tax at a rate of $31\%$ has purchased the bond at issue and held it to redemption.

Interest and capital payments were indexed by reference to the value of an inflation index with a time lag of $6$ months. The value of the inflation indexes at various dates during the term of the loan were as follows:

Inflation indexes for

$2016-2020$

$,2016,2017,2018,2019,2020$

January $103\mathrm{.}6,109\mathrm{.}2,117,123\mathrm{.}5,129\mathrm{.}3$

July $01\mathrm{.}8,108\mathrm{.}2,112\mathrm{.}1,120\mathrm{.}5,125\mathrm{.}5$

Calculate the price paid at issue for the bond, given that the investor has achieved an effective money yield of $6\mathrm{.}2\%$ per annum from this investment.