$*9.$ Under an annuity$-$certain payable continuously for $10$ years, payments are

made at the rate of $1$ per annum for the first $3$ months, $2$ per annum for the

next $3$ months, $3$ per annum for the next $3$ months and so on$.$ To what

amount will the annuity payments accumulate by the end of the $10$ years

assuming interest at $10\%$ per annum convertible half$-$yearly?