At an effective annual interest rate j$,$ the following options are the same: i$)$ A payment of $10,000$ at the beginning of the seventh year.

i$)$ A payment of $10,000$ at the beginning of the seventh year.

ii$)$ A payment of $6,000$ at the end of year t and $56,000$ at the end of year $2.$

iii$)$ An immediate payment of $$5,000.$

Using the semiannual effective rate of interest equivalent of j$.$ Calculate the present value of a payment of $8,000$ at the beginning of year t $+4.$