Lock in rate and FRA

1) in calculation of lock in rate
if spot rate is lower than future , why it is that current future rate – basis
rather than adding the basis?

I thought the on the transaction date,
the future price (agreed rate in the future time) is bigger so that
it is appropriate to add the basis from the current future price
to calculate future price on the transaction date.

thank you for help:)

2) FRA
this is june 05 question

Requirements

now is 1june and receive 7.1m in 5month and invest for four month
Futures contracts mature at end of month and SIBOR is currently at 4%
The current yield on high quality commercial paper is SIBOR+0.6%

Position is investor who is afraid for interest rate to go down.
so need to sell FRA , buy futures and options
FRA prices:
5 v 9 3.5 -3.45
If SIBOR fell by 0.5% during 5 months

?? question is i thought
it is required to know the SIBOR in 5month times

then i thought
Investement
$7.1m x 4.1%x 4/12

Profit or loss on FRA
$7.1m x(3.5%(OFFER RATE Due to selling the FRA) less 3.5 % (to buy back))x 4/12

But ANSWER is,
Investement
$7.1m x( 4.1%= 3.5 +0.6% )x 4/12 = 0.97033

Profit or loss on FRA
$7.1m x(3.5%(SELL RATE) – 3.45% )x 4/12 X (1 /(1+(3.5%X 4/12))

I thought on the basis from the lecture of p4 in open tuition
1) transaction at risk 2) profit or loss
but the profit and loss part can be calculated by using the formular but
it is hard to understand why profit and loss could be calculated from directly bid and sell rate based on same date?

Really appreciate for the help.
thank you!