Consider a contract entitling your friend to an infinite series of payments into their bank account, such that in year t. they receive / (t) dollars, with interest compounded continuously. Suppose that you want to buy the contract from your friend, so that you will receive the payments instead. What price should you pay for it? As a payment received now is worth more than a payment received in the future, the answer is not obvious. It turns out that the answer is an integral. The present value of the payment stream is I(tje at dt. where o is the discount rate. The discount rate is a number that measures how much more valuable it is to receive money now versus in the future