The 9-month Libor rate is 4%. The 12-month Libor rate is 5%. An investor creating a homemade forward forward could earn what annualized interest rate on a 3-month $1,000,000 deposit made in 9 months?

I'm pretty confident it is:

1,000,000 / 1 + .04 (3/4) = $970,874

$970,874 x (1 + .05 (4/4)) = $1,019,418

then this is where I'm unsure... is it:

$1,019,418 - $970,874 = $48,544

$48,544 / $1,000,000 = .0485 = 4.85%

Please show work if this isn't right