Futures and options

Hello Mr John. I was watching your videos on how to calculate the lock in rate .

This is part of the question I saw in kaplan

Chesterfield Co needs to borrow $5 million for 6 months, starting in
4 months’ time on 1st August.
The current SOFR rate is 3.50% but there is a risk that interest rates will
change over the next few months by up to 0.5% either way, so the
company’s treasurer is considering hedging the interest payments using
futures contracts or options. Chesterfield Co can borrow at 25 basis
points above the SOFR rate.
Current futures/options information:
Futures ($500,000 3 month contracts)
June 96.40
September 96.10
December 95.86

My calculations
61/153 × 0. 40 =0.16

Their answer is 0.13 I wonder where I got it wrong.
Please help.

answer

Basis workings:
1 April 1 August 30 Sept
SOFR 3.50%
(i.e. 96.50)
Futures price 96.10
Basis 0.40% 0.13% (W2) 0 (W1)
(W1) Basis will reduce to zero by the expiry date of the contract, because
on that date, the futures price will equal 100 – the (known) SOFR
rate.
(W2) Assuming basis reduces in a linear manner, the basis at 1 August
should be 2/6 of the original 0.40% i.e. 0.13%.
From this information we can derive the lock-in rate as
100 – (current futures price + unexpired basis on the transaction date)
= 100 – (96.10 + 0.13%) = 3.77%

They are saying the basis from 1 August is 2/6
I don’t understand where they got that from