Is it possible for a person to know now if he/she is saved and would be inheriting eternal life in the hereafter as per the Biblical teachings?

There is an important difference between hoping, and knowing (while in this world, regarding a place in Janna or Paradise). To hope is not to know. And there are two important problems. What pious, Bible-believing Christians call "the assurance of salvation", many others call presumptuousness, because they do not have such an assurance. The problem is explaining what enables some to speak confidently of being with Christ in glory after they have died, and how others interpret the many Bible promises that are meant to assure Christians of this.

Problem #1 cannot be solved by listing the many scriptures in the Bible that speak of future glory as assured, but you have asked for that, so I will list a small sample of some of the texts (hoping that other answers will provide ones I've missed out due to the huge amount of space a full list would take up):

“And as many as were ordained to eternal life believed.” Acts 13:48

“And you were made alive, you who were dead in your transgressions and sins in which you used to live… But because of his great love for us, God, who is rich in mercy, made us alive with Christ even when we were dead in transgressions – it is by grace you have been saved… For it is by grace you are saved, through faith – and this not from yourselves, it is the gift of God – not by works, so that no-one can boast. For we are God’s workmanship, created in Christ Jesus to do good works which God prepared in advance for us to do.” Ephesians 2:1-10

“Being confident of this, that he who began a good work in you will carry it on to completion until the day of Christ Jesus... now as always, Christ will be exalted in my body, whether by life or by death. For to me, to live is Christ and to die is gain... Yet what shall I choose? I do not know! I am torn between the two; I desire to depart and be with Christ, which is better by far. ” Philippians 1:5 & 20-24

“For God did not appoint us to suffer wrath but to receive salvation through our Lord Jesus Christ… May God himself, the God of peace, sanctify you through and through. May your whole spirit, soul and body be kept blameless at the coming of our Lord Jesus Christ. The one who calls you is faithful and he will do it.” 1 Thessalonians 5:9 & 22-24

“He will keep you strong to the end, so that you will be blameless on the day of our Lord Jesus Christ. God, who has called you into fellowship with his Son Jesus Christ our Lord, is faithful.” 1 Corinthians 1:8-9

“By one sacrifice he has made perfect for ever those who are being made holy.” Hebrews 10:14

"Now we know that if the earthly tent we live in is destroyed, we have a building from God, an eternal house in heaven... Now it is God who has made us for this very purpose and has given us the Spirit as a deposit, guaranteeing what is to come. Therefore we are always confident and know that as long as we are at home in the body we are away from the Lord. We live by faith, not by sight. We are confident..." [All italics mine.]

Problem #2 prevents those who do not have this confidence in the promises and assurances of God from understanding why others do. They accept interpretations of all those promises that they are provisional, dependent on the believer not slipping up badly enough before death, so as to forfeit everything. And, to be fair, there are, indeed some Bible texts that they protest show this. For example, Philippians 2:12 & Hebrews 10:26-39 to mention but two. To save the question degenerating into trading proof-texts, there is a simple solution to both problems.

The solution lies in knowing what the Bible means when it says the Holy Spirit has been given to saved believers, as a guarantee that they are now adopted into God's family, and are sons who will obtain the promised heavenly inheritance. Romans chapter 8 explains this fully. Sadly, many professed Christians have no idea what that chapter means, experientially, because they are not anointed, or indwelt, with the Holy Spirit. Many have been told that such an assurance is limited to a tiny number of people, or they have been told that it's a provisional guarantee (which is a contradiction in terms) and think no further, because they don't have that assurance from the Holy Spirit.

There's nothing anybody can do about this. You either have the Holy Spirit's assurance, or you don't. I cannot offer you proofs. I cannot argue and argue about proof-texts, nor would I. That is futile. Yet that is what this question will likely descend into. So, let people call the assured saints 'presumptuous' if they want. That won't change the material fact of them being securely in Christ's hand, which is the same as being in the hand of the Father (as Jesus said, John 10:27-30). They know that nothing can now separate them from the love of God in Christ (Romans 8:29-35).