To solve this problem, we can break it down into two parts:

Calculate the future value of the initial investment at $9\%$ p$.$a$.$ compound interest for $5$ years.

Calculate the future value of the remaining balance at $13\%$ p$.$a$.$ interest, compounded semi$-$annually for $4$ years.

Part $1$: Future Value of Initial Investment

We can use the formula for the future value of an ordinary annuity to calculate the future value of the annual investments at $9\%$ p$.$a$.$ compound interest for $5$ years.

The formula for the future value of an ordinary annuity is:

FV $=$ P $*[(1+$ r$)^$n $-1]/$ r

Where:

FV $=$ Future Value

P $=$ Annual payment

r $=$ Interest rate per period

n $=$ Number of periods

Using the given values:

P $=$ R$1000$

r $=9\%$ p$.$a$.=0\mathrm{.}09$

n $=5$ years

We can calculate the future value of the initial investment.

Part $2$: Future Value of Remaining Balance

For the remaining balance, we can use the compound interest formula:

A $=$ P$(1+$ r$/$n$)^($nt$)$

Where:

A $=$ the amount of money accumulated after n years, including interest.

P $=$ the principal amount $($initial amount of money$).$

r $=$ annual interest rate $($in decimal$).$

n $=$ number of times that interest is compounded per year.

t $=$ time the money is invested for in years.

Using the given values:

P $=$ R$984\mathrm{.}71$

r $=13\%$ p$.$a$.=0\mathrm{.}13$

n $=2($compounded semi$-$annually$)$

t $=4$ years

We can calculate the future value of the remaining balance.