这意味着银行贷款的总金额为：T = A *（1-r）1 + A *（1-r）2 + A *（1-r）3 + ……每个时期到无穷大。显然，我们不能直接计算银行每期贷款的金额，并将它们全部加在一起，因为有无限数量的条款。然而，从数学我们知道以下关系适用于无穷级数：x1 + x2 + x3 + x4 + … = x /（1-x）请注意，在我们的等式中，每个项都乘以A.如果我们将其作为公共因子，我们得到：T = A [（1-r）1 +（1-r）2 +（1-r）3 +。 ..]请注意，方括号中的术语与我们无限的x项系列相同，其中（1-r）代替x。如果我们用（1-r）替换x，则系列等于（1-r）/（1 – （1-r）），这简化为1 / r – 1.因此银行贷出的总金额是：T = A *（1 / r – 1）因此，如果A = 200亿且r = 20％，则银行贷款的总额为：T = 200亿美元*（1 / 0.2-1）= 800亿美元。回想一下，借出的所有资金最终都会被放回银行。如果我们想知道总存款增加了多少，我们还需要包括存入银行的200亿美元。所以总增加额为1000亿美元。
英国曼彻斯特大学会计论文代写：银行贷款
This means that the total amount of bank loans is: T = A *(1-r)1 + A *(1-r)2 + A *(1-r)3 + ……Every period to infinity. Obviously, we can’t directly calculate the amount of each bank loan and add them all together because there are an unlimited number of terms. However, from mathematics we know that the following relationship applies to infinite series: x1 + x2 + x3 + x4 + … = x /(1-x)Note that in our equation, each term is multiplied by A. If we take it as a common factor, we get: T = A [(1-r)1 +(1-r)2 +(1- r) 3 +. ..]Note that the terms in square brackets are the same as our infinite series of x items, where (1-r) replaces x. If we replace x with (1-r), the series is equal to (1-r)/(1 – (1-r)), which is reduced to 1 / r – 1. So the total amount of bank lending is:T = A *(1 / r – 1) Therefore, if A = 20 billion and r = 20%, the total amount of bank loans is: T = $20 billion * (1 / 0.2-1) = $80 billion. Recall that all the funds borrowed will eventually be returned to the bank. If we want to know how much the total deposit has increased, we also need to include $20 billion in deposits into the bank. So the total increase is 100 billion US dollars.